{"id":37674,"date":"2025-02-02T08:01:03","date_gmt":"2025-02-02T00:01:03","guid":{"rendered":"https:\/\/17aitech.com\/?p=37674"},"modified":"2025-02-02T08:01:03","modified_gmt":"2025-02-02T00:01:03","slug":"%e5%a6%82%e4%bd%95%e8%af%81%e6%98%8e%e4%b8%80%e4%b8%aa%e6%95%b0%e6%98%af%e6%97%a0%e7%90%86%e6%95%b0%ef%bc%9f%e4%bb%96%e4%bb%ac%e6%89%be%e5%88%b0%e4%ba%86%e6%ac%a7%e6%8b%89%e5%92%8c%e9%bb%8e%e6%9b%bc","status":"publish","type":"post","link":"https:\/\/17aitech.com\/?p=37674","title":{"rendered":"\u5982\u4f55\u8bc1\u660e\u4e00\u4e2a\u6570\u662f\u65e0\u7406\u6570\uff1f\u4ed6\u4eec\u627e\u5230\u4e86\u6b27\u62c9\u548c\u9ece\u66fc\u9519\u8fc7\u7684\u8bc1\u660e\uff0c\u534e\u4eba\u6570\u5b66\u5bb6\u5510\u4e91\u6e05\u53c2\u4e0e"},"content":{"rendered":"<p>\u6587\u7ae0\u6765\u6e90\u4e8e\u4e92\u8054\u7f51:<a href=\"https:\/\/www.jiqizhixin.com\/articles\/2025-01-09-13\" target=\"_blank\">\u5982\u4f55\u8bc1\u660e\u4e00\u4e2a\u6570\u662f\u65e0\u7406\u6570\uff1f\u4ed6\u4eec\u627e\u5230\u4e86\u6b27\u62c9\u548c\u9ece\u66fc\u9519\u8fc7\u7684\u8bc1\u660e\uff0c\u534e\u4eba\u6570\u5b66\u5bb6\u5510\u4e91\u6e05\u53c2\u4e0e<\/a><\/p>\n<p>\u6211\u4eec\u90fd\u77e5\u9053\uff0c\u5b9e\u6570\u5206\u4e3a\u6709\u7406\u6570\u548c\u65e0\u7406\u6570\uff0c\u5b83\u4eec\u7684\u5b9a\u4e49\u4e5f\u90fd\u5f88\u660e\u786e\u3002\u4f46\u4ee4\u4eba\u60ca\u8bb6\u7684\u662f\uff0c\u5176\u5b9e\u5f88\u96be\u8bc1\u660e\u4e00\u4e2a\u6570\u7a76\u7adf\u80fd\u5426\u5199\u6210\u5206\u6570\u5f62\u5f0f\u3002\u800c\u73b0\u5728\uff0c\u8fd9\u4e2a\u53e4\u8001\u7684\u95ee\u9898\u6709\u4e86\u4e00\u79cd\u5e7f\u6cdb\u9002\u7528\u7684\u65b0\u65b9\u6cd5\u3002<\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-17c11a8a7a9762083850a5891aca5808.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-17c11a8a7a9762083850a5891aca5808.png\"><\/a><\/section>\n<section>\u8fd9\u79cd\u65b0\u65b9\u6cd5\u6709\u4e09\u4f4d\u63d0\u51fa\u8005\uff0c\u5206\u522b\u662f\u829d\u52a0\u54e5\u5927\u5b66\u7684\u6570\u8bba\u548c\u6717\u5170\u5179\u7eb2\u9886\u6570\u5b66\u6559\u6388 Frank Calegari\u3001\u52a0\u5dde\u7406\u5de5\u5b66\u9662\u6570\u5b66\u6559\u6388 Vesselin Dimitrov\u3001\u52a0\u5dde\u5927\u5b66\u4f2f\u514b\u5229\u5206\u6821\u52a9\u7406\u6559\u6388\u53ca 2022 \u5e74\u62c9\u9a6c\u52aa\u91d1\u5956\u5f97\u4e3b\u5510\u4e91\u6e05\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-630f3c1a3ed1f9c6ab4a89a5230913a9.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-630f3c1a3ed1f9c6ab4a89a5230913a9.png\"><\/a><\/section>\n<section><em><sup>\u5510\u4e91\u6e05\uff0c<\/sup><\/em><sup><em>\u52a0\u5dde\u5927\u5b66\u4f2f\u514b\u5229\u5206\u6821\u52a9\u7406\u6559\u6388\uff0c<\/em><\/sup><em><sup>\u672c\u79d1\u6bd5\u4e1a\u4e8e\u5317\u4eac\u5927\u5b66\u6570\u5b66\u79d1\u5b66\u5b66\u9662\uff0c\u540e\u5728\u54c8\u4f5b\u5927\u5b66\u53d6\u5f97\u6570\u5b66\u535a\u58eb\u5b66\u4f4d\uff0c2022 \u5e74\u6210\u4e3a\u9996\u4f4d\u83b7\u62c9\u9a6c\u52aa\u91d1\u5956\u7684\u534e\u4eba\u5973\u6570\u5b66\u5bb6\u3002<\/sup><\/em><\/section>\n<section><\/section>\n<section>\u91cf\u5b50\u6742\u5fd7\u4f5c\u8005 Erica Klarreich \u8fd1\u65e5\u53d1\u6587\u4ecb\u7ecd\u4e86\u8fd9\u79cd\u65b0\u65b9\u6cd5\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-013b18e9fe47dcb8b3612e3825a33e0b.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-013b18e9fe47dcb8b3612e3825a33e0b.png\"><\/a><\/section>\n<section>\u539f\u6587\u5730\u5740\uff1ahttps:\/\/www.quantamagazine.org\/rational-or-not-this-basic-math-question-took-decades-to-answer-20250108\/<\/section>\n<section><\/section>\n<section>1978 \u5e74 6 \u6708\uff0c\u5728\u6cd5\u56fd\u9a6c\u8d5b\u4e3e\u529e\u7684\u4e00\u573a\u5927\u578b\u6570\u5b66\u4f1a\u8bae\u4e0a\uff0c\u4e3b\u529e\u65b9\u6700\u540e\u4e00\u523b\u8865\u5145\u4e86\u4e00\u4e2a\u65e5\u7a0b\u3002\u5728\u5348\u9910\u65f6\u95f4\uff0c\u6570\u5b66\u5bb6\u7f57\u6770\u30fb\u963f\u57f9\u91cc\uff08Roger Ap\u00e9ry\uff09\u5c06\u5c55\u793a\u4e00\u4e2a\u8bc1\u660e\uff0c\u8bc1\u660e\u6570\u5b66\u4e2d\u6700\u8457\u540d\u7684\u6570\u4e4b\u4e00 \u2014\u2014zeta of 3\uff0c\u6570\u5b66\u5bb6\u5199\u4f5c \u03b6(3)\u2014\u2014 \u4e0d\u80fd\u8868\u793a\u4e3a\u4e24\u4e2a\u975e\u8d1f\u6574\u6570\u6784\u6210\u7684\u5206\u6570\u3002\u8fd9\u4e2a\u6570\u662f\u6570\u5b66\u5bb6\u6240\u8bf4\u7684\u300c\u65e0\u7406\u6570\u300d\u3002<\/section>\n<section><\/section>\n<section>\u4e0e\u4f1a\u8005\u90fd\u6301\u6000\u7591\u6001\u5ea6\u3002\u9ece\u66fc zeta \u51fd\u6570\uff08Riemann zeta function\uff09\u662f\u6570\u8bba\u4e2d\u6700\u6838\u5fc3\u7684\u51fd\u6570\u4e4b\u4e00\uff0c\u6570\u5b66\u5bb6\u4eec\u51e0\u4e2a\u4e16\u7eaa\u4ee5\u6765\u4e00\u76f4\u5728\u8bd5\u56fe\u8bc1\u660e \u03b6(3) \u7684\u65e0\u7406\u6027 \u2014\u2014 \u8fd9\u4e2a\u6570\u662f\u8f93\u5165\u4e3a 3 \u65f6 zeta \u51fd\u6570\u7684\u8f93\u51fa\u503c\u3002\u5f53\u65f6 61 \u5c81\u7684\u963f\u57f9\u91cc\u5e76\u4e0d\u88ab\u5e7f\u6cdb\u8ba4\u4e3a\u662f\u9876\u5c16\u6570\u5b66\u5bb6\u3002\u4ed6\u6709\u7740\u6cd5\u56fd\u4e61\u4e0b\u4eba\u7684\u53e3\u97f3\uff0c\u8fd8\u6709\u7740\u7231\u6311\u8845\u7684\u540d\u58f0\u3002\u8bb8\u591a\u4e0e\u4f1a\u8005\u8ba4\u4e3a\u963f\u57f9\u91cc\u5728\u73a9\u4e00\u4e2a\u7cbe\u5fc3\u7b56\u5212\u7684\u6076\u4f5c\u5267\uff0c\u4ed6\u4eec\u51c6\u5907\u4ee5\u5176\u4eba\u4e4b\u9053\u8fd8\u6cbb\u5176\u4eba\u4e4b\u8eab\u3002\u6b63\u5982\u4e00\u4f4d\u6570\u5b66\u5bb6\u540e\u6765\u56de\u5fc6\u7684\u90a3\u6837\uff0c\u4ed6\u4eec\u300c\u662f\u6765\u6363\u4e71\u7684\u300d\u3002<\/section>\n<section><\/section>\n<section>\u8fd9\u573a\u6f14\u8bb2\u5f88\u5feb\u9677\u5165\u6df7\u4e71\u3002\u963f\u57f9\u91cc\u51e0\u4e4e\u6ca1\u6709\u89e3\u91ca\u5c31\u4e00\u4e2a\u63a5\u4e00\u4e2a\u5730\u5c55\u793a\u65b9\u7a0b\uff0c\u5176\u4e2d\u4e00\u4e9b\u6d89\u53ca\u4e0d\u53ef\u80fd\u7684\u8fd0\u7b97\uff0c\u6bd4\u5982\u9664\u4ee5\u96f6\u3002\u5f53\u88ab\u95ee\u53ca\u8fd9\u4e9b\u516c\u5f0f\u4ece\u4f55\u800c\u6765\u65f6\uff0c\u4ed6\u58f0\u79f0\uff1a\u300c\u5b83\u4eec\u662f\u5728\u6211\u7684\u82b1\u56ed\u957f\u51fa\u6765\u7684\u3002\u300d\u6570\u5b66\u5bb6\u4eec\u5bf9\u4ed6\u7684\u8bba\u65ad\u62a5\u4ee5\u5927\u7b11\uff0c\u5728\u623f\u95f4\u91cc\u5411\u670b\u53cb\u4eec\u558a\u8bdd\uff0c\u8fd8\u6254\u7eb8\u98de\u673a\u3002<\/section>\n<section><\/section>\n<section>\u4f46\u81f3\u5c11\u6709\u4e00\u4e2a\u4eba\uff0c\u5373\u73b0\u5728\u6ce2\u5c14\u591a\u5927\u5b66\u7684\u4ea8\u5229\u30fb\u79d1\u6069\uff08Henri Cohen\uff09\uff0c\u4ece\u6f14\u8bb2\u4e2d\u786e\u4fe1\u963f\u57f9\u91cc\u662f\u5bf9\u7684\u3002\u79d1\u6069\u7acb\u5373\u7740\u624b\u5145\u5b9e\u963f\u57f9\u91cc\u8bba\u8bc1\u7684\u7ec6\u8282\uff1b\u5728\u51e0\u4e2a\u6708\u65f6\u95f4\u5185\uff0c\u4ed6\u4e0e\u5176\u4ed6\u51e0\u4f4d\u6570\u5b66\u5bb6\u4e00\u8d77\u5b8c\u6210\u4e86\u8bc1\u660e\u3002\u5f53\u4ed6\u5728\u540e\u6765\u7684\u4e00\u6b21\u4f1a\u8bae\u4e0a\u5c55\u793a\u4ed6\u4eec\u7684\u7ed3\u8bba\u65f6\uff0c\u4e00\u4f4d\u542c\u4f17\u62b1\u6028\u9053\uff1a\u300c\u8fd9\u662f\u6cd5\u56fd\u519c\u6c11\u7684\u80dc\u5229\u3002\u300d<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-c0f94c91998b3259bab2d6d2959d3846.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-c0f94c91998b3259bab2d6d2959d3846.png\"><\/a><\/section>\n<section><em><sup>\u5f53\u7f57\u6770\u30fb\u963f\u57f9\u91cc\u5ba3\u5e03\u4ed6\u5df2\u7ecf\u8bc1\u660e\u4e86 \u03b6(3) \u7684\u65e0\u7406\u6027\u65f6\uff0c\u6570\u5b66\u5bb6\u4eec\u5bf9\u4ed6\u55e4\u4e4b\u4ee5\u9f3b\uff0c\u5e76\u5411\u4ed6\u6254\u7eb8\u98de\u673a\u3002\u4f46\u4e8b\u5b9e\u8bc1\u660e\u4ed6\u662f\u5bf9\u7684\u3002\u4ed6\u5728\u5df4\u9ece\u7684\u5893\u7891\u4e0a\u5c31\u523b\u6709\u8fd9\u6761\u5b9a\u7406\u3002<\/sup><\/em><\/section>\n<section><\/section>\n<section>\u6570\u5b66\u5bb6\u4eec\u867d\u7136\u4e0d\u60c5\u613f\u4f46\u8fd8\u662f\u63a5\u53d7\u4e86\u963f\u57f9\u91cc\u7684\u8bc1\u660e\uff0c\u4ed6\u4eec\u8fd8\u9884\u8ba1\u4f1a\u51fa\u73b0\u5927\u91cf\u65e0\u7406\u6570\u7684\u8bc1\u660e\u7ed3\u679c\u3002<\/section>\n<section><\/section>\n<section>\u65e0\u7406\u6570\u8fdc\u6bd4\u6709\u7406\u6570\u591a\uff1a\u5982\u679c\u4f60\u5728\u6570\u8f74\u4e0a\u968f\u673a\u9009\u62e9\u4e00\u4e2a\u70b9\uff0c\u5b83\u51e0\u4e4e\u5fc5\u5b9a\u662f\u65e0\u7406\u6570\u3002\u5373\u4f7f\u6570\u5b66\u7814\u7a76\u4e2d\u51fa\u73b0\u7684\u6570\u5b57\u4ece\u5b9a\u4e49\u4e0a\u6765\u8bf4\u5e76\u975e\u968f\u673a\uff0c\u4f46\u6570\u5b66\u5bb6\u4eec\u4ecd\u7136\u8ba4\u4e3a\u5b83\u4eec\u4e2d\u7684\u5927\u591a\u6570\u5e94\u8be5\u662f\u65e0\u7406\u6570\u3002\u4f46\u662f\uff0c\u867d\u7136\u6570\u5b66\u5bb6\u4eec\u6210\u529f\u5730\u8bc1\u660e\u4e86\u67d0\u4e9b\u6570\u7684\u8fd9\u4e2a\u57fa\u672c\u4e8b\u5b9e\uff0c\u6bd4\u5982 \u03c0 \u548c e\uff0c\u4f46\u5bf9\u4e8e\u5927\u591a\u6570\u5176\u4ed6\u6570\u6765\u8bf4\uff0c\u8bc1\u660e\u4ecd\u7136\u6781\u5176\u56f0\u96be\u3002\u6570\u5b66\u5bb6\u4eec\u5e0c\u671b\uff0c\u4ece \u03b6(3) \u4e4b\u5916\u7684 zeta \u51fd\u6570\u7684\u5176\u4ed6\u503c\u5f00\u59cb\uff0c\u963f\u57f9\u91cc\u7684\u6280\u672f\u53ef\u80fd\u6700\u7ec8\u80fd\u8ba9\u4ed6\u4eec\u53d6\u5f97\u8fdb\u5c55\u3002<\/section>\n<section><\/section>\n<section>\u8377\u5170\u62c9\u5fb7\u5821\u5fb7\u5927\u5b66\u7684 Wadim Zudilin \u8bf4\uff1a\u300c\u5f53\u65f6\u6bcf\u4e2a\u4eba\u90fd\u76f8\u4fe1\u53ea\u9700\u4e00\u4e24\u5e74\u65f6\u95f4\uff0c\u5c31\u80fd\u8bc1\u660e\u6bcf\u4e2a zeta \u503c\u90fd\u662f\u65e0\u7406\u6570\u3002\u300d<\/section>\n<section><\/section>\n<section>\u4f46\u9884\u671f\u7684\u7a81\u7834\u5e76\u672a\u51fa\u73b0\u3002\u6ca1\u6709\u4eba\u771f\u6b63\u7406\u89e3\u963f\u57f9\u91cc\u7684\u516c\u5f0f\u662f\u4ece\u54ea\u91cc\u6765\u7684\uff0c\u800c\u4e14\u5f53\u300c\u4f60\u6709\u4e00\u4e2a\u5982\u6b64\u964c\u751f\u7684\u8bc1\u660e\u65f6\uff0c\u8981\u6cdb\u5316\u3001\u91cd\u590d\u8fd9\u79cd\u9b54\u6cd5\u5e76\u4e0d\u603b\u662f\u90a3\u4e48\u5bb9\u6613\uff0c\u300d\u829d\u52a0\u54e5\u5927\u5b66\u7684 Frank Calegari \u8bf4\u3002\u6570\u5b66\u5bb6\u4eec\u5f00\u59cb\u628a\u963f\u57f9\u91cc\u7684\u8bc1\u660e\u89c6\u4e3a\u4e00\u4e2a\u5b64\u7acb\u7684\u5947\u8ff9\u3002<\/section>\n<section><\/section>\n<section>\u4f46\u73b0\u5728\uff0cCalegari \u548c\u53e6\u5916\u4e24\u4f4d\u6570\u5b66\u5bb6 \u2014\u2014 \u52a0\u5dde\u7406\u5de5\u5b66\u9662\u7684 Vesselin Dimitrov \u548c\u52a0\u5dde\u5927\u5b66\u4f2f\u514b\u5229\u5206\u6821\u7684\u5510\u4e91\u6e05\uff08Yunqing Tang\uff09\u2014\u2014 \u505a\u5230\u4e86\uff01\u4ed6\u4eec\u6210\u529f\u5c55\u793a\u4e86\u53ef\u4ee5\u5982\u4f55\u5c06\u963f\u57f9\u91cc\u7684\u65b9\u6cd5\u62d3\u5c55\u4e3a\u4e00\u4e2a\u66f4\u5f3a\u5927\u7684\u65b9\u6cd5\u6765\u8bc1\u660e\u6570\u7684\u65e0\u7406\u6027\u3002\u4f7f\u7528\u8fd9\u79cd\u65b9\u6cd5\uff0c\u4ed6\u4eec\u8bc1\u660e\u4e86\u65e0\u9650\u591a\u4e2a\u7c7b\u4f3c zeta \u7684\u503c\u7684\u65e0\u7406\u6027\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-39b618e5db149b08ed33b41679e79659.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-39b618e5db149b08ed33b41679e79659.png\"><\/a><\/section>\n<section>\u8bba\u6587\u5730\u5740\uff1ahttps:\/\/arxiv.org\/pdf\/2408.15403<\/section>\n<section><\/section>\n<section>\u5df4\u9ece &#8211; \u8428\u514b\u96f7\u5927\u5b66\u7684 Jean-Beno\u00eet Bost \u79f0\u4ed6\u4eec\u7684\u53d1\u73b0\u662f\u300c\u6570\u8bba\u9886\u57df\u7684\u4e00\u4e2a\u660e\u663e\u7a81\u7834\u300d\u3002<\/section>\n<section><\/section>\n<section>\u6570\u5b66\u5bb6\u4eec\u5174\u594b\u7684\u4e0d\u4ec5\u662f\u8fd9\u4e9b\u7ed3\u679c\uff0c\u8fd8\u6709\u7814\u7a76\u8005\u7684\u65b9\u6cd5\u3002\u4ed6\u4eec\u5728 2021 \u5e74\u7528\u8fd9\u79cd\u65b9\u6cd5\u89e3\u51b3\u4e86\u4e00\u4e2a\u5df2\u6709 50 \u5e74\u5386\u53f2\u7684\u731c\u60f3\uff0c\u8be5\u731c\u60f3\u4e0e\u6570\u8bba\u4e2d\u6240\u8c13\u7684\u6a21\u5f62\u5f0f\uff08modular forms\uff09\u6709\u5173\u3002<\/section>\n<section><\/section>\n<section>\u300c\u4e5f\u8bb8\u73b0\u5728\u6211\u4eec\u5df2\u6709\u8db3\u591f\u7684\u5de5\u5177\uff0c\u53ef\u4ee5\u5c06\u8fd9\u7c7b\u4e3b\u9898\u63a8\u8fdb\u5230\u6bd4\u4ee5\u524d\u8ba4\u4e3a\u53ef\u80fd\u7684\u66f4\u8fdc\u7684\u5730\u65b9\uff0c\u300d\u5df4\u9ece\u9ad8\u7b49\u5e08\u8303\u5b66\u9662\u7684 Fran\u00e7ois Charles \u8bf4\u3002\u300c\u8fd9\u662f\u4e00\u4e2a\u975e\u5e38\u4ee4\u4eba\u5174\u594b\u7684\u65f6\u671f\u3002\u300d<\/section>\n<section><\/section>\n<section>\u867d\u7136\u963f\u57f9\u91cc\u7684\u8bc1\u660e\u4f3c\u4e4e\u51ed\u7a7a\u800c\u6765\uff0c\u751a\u81f3\u4e00\u4f4d\u6570\u5b66\u5bb6\u5c06\u5176\u79f0\u4e3a\u300c\u5947\u8ff9\u548c\u795e\u79d8\u7684\u6df7\u5408\u300d\u2014\u2014 \u4f46\u8fd9\u7bc7\u65b0\u8bba\u6587\u5c06\u4ed6\u7684\u65b9\u6cd5\u7eb3\u5165\u4e86\u4e00\u4e2a\u5e7f\u6cdb\u9002\u7528\u7684\u6846\u67b6\u3002\u6e05\u6670\u5ea6\u5927\u5927\u63d0\u5347\uff0c\u56e0\u6b64\u4eba\u4eec\u4e0d\u7981\u60f3\uff0cCalegari\u3001Dimitrov \u548c\u5510\u4e91\u6e05\u7684\u7ed3\u679c\u53ef\u4ee5\u66f4\u5bb9\u6613\u50ac\u751f\u8fdb\u4e00\u6b65\u7684\u6210\u679c\u3002<\/section>\n<section><\/section>\n<section>\u591a\u4f26\u591a\u5927\u5b66\u7684 Daniel Litt \u8bf4\uff1a\u300c\u5e0c\u671b\u6211\u4eec\u5f88\u5feb\u5c31\u4f1a\u770b\u5230\u76f8\u5173\u65e0\u7406\u6027\u8bc1\u660e\u7684\u6dd8\u91d1\u70ed\u3002\u300d<\/section>\n<section><\/section>\n<section><strong>\u6b27\u62c9\u9519\u8fc7\u7684\u8bc1\u660e<\/strong><\/section>\n<section><\/section>\n<section>\u81ea\u6570\u5b66\u53d1\u73b0\u7684\u6700\u65e9\u65f6\u671f\u4ee5\u6765\uff0c\u4eba\u4eec\u5c31\u4e00\u76f4\u5728\u95ee\u54ea\u4e9b\u6570\u5b57\u662f\u6709\u7406\u6570\u3002\u4e24\u5343\u4e94\u767e\u5e74\u524d\uff0c\u6bd5\u8fbe\u54e5\u62c9\u65af\u5b66\u6d3e\u575a\u4fe1\u6bcf\u4e2a\u6570\u90fd\u662f\u4e24\u4e2a\u6574\u6570\u7684\u6bd4\u503c\u3002\u5f53\u4ed6\u4eec\u5b66\u6d3e\u7684\u4e00\u540d\u6210\u5458\u8bc1\u660e 2 \u7684\u5e73\u65b9\u6839\u4e0d\u662f\u6709\u7406\u6570\u65f6\uff0c\u4ed6\u4eec\u9707\u60ca\u4e86\u3002\u4f20\u8bf4\u4f5c\u4e3a\u60e9\u7f5a\uff0c\u8fd9\u4f4d\u5192\u72af\u8005\u88ab\u6df9\u6b7b\u4e86\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-e4c498a8348efbad643ead6958941863.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-e4c498a8348efbad643ead6958941863.png\"><\/a><\/section>\n<section>2 \u7684\u5e73\u65b9\u6839\u53ea\u662f\u4e2a\u5f00\u59cb\u3002\u7279\u6b8a\u7684\u6570\u4ece\u6570\u5b66\u63a2\u7a76\u7684\u6240\u6709\u9886\u57df\u4e0d\u65ad\u6d8c\u73b0\u3002\u6709\u4e9b\u6570\uff0c\u6bd4\u5982 \u03c0\uff0c\u5728\u4f60\u8ba1\u7b97\u9762\u79ef\u548c\u4f53\u79ef\u65f6\u51fa\u73b0\u3002\u5176\u4ed6\u7684\u5219\u4e0e\u7279\u5b9a\u51fd\u6570\u76f8\u8fde \u2014\u2014 \u4f8b\u5982\uff0ce \u662f\u81ea\u7136\u5bf9\u6570\u7684\u5e95\u6570\u3002\u300c\u8fd9\u662f\u4e00\u4e2a\u6311\u6218\uff1a\u4f60\u7ed9\u81ea\u5df1\u4e00\u4e2a\u5728\u6570\u5b66\u4e2d\u81ea\u7136\u51fa\u73b0\u7684\u6570\uff0c[\u7136\u540e] \u4f60\u60f3\u77e5\u9053\u5b83\u662f\u5426\u662f\u6709\u7406\u6570\uff0c\u300d\u79d1\u6069\u8bf4\u3002\u300c\u5982\u679c\u4e00\u4e2a\u6570\u662f\u6709\u7406\u6570\uff0c\u90a3\u5b83\u5c31\u4e0d\u662f\u4e00\u4e2a\u5f88\u6709\u8da3\u7684\u6570\u3002\u300d<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-e58fb39b1440b45eb8b3dd298f52345a.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-e58fb39b1440b45eb8b3dd298f52345a.png\"><\/a><\/section>\n<section><em><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Frank Calegari \u6b63\u5728\u6f14\u8bb2\u3002\u4ed6\u4e0e\u53e6\u5916\u4e24\u4f4d\u5408\u4f5c\u8005\u4e00\u8d77\u5f97\u5230\u7684\u8bc1\u660e\u53ef\u671b\u5f15\u53d1\u65e0\u7406\u6027\u8bc1\u660e\u7684\u6dd8\u91d1\u70ed\u3002<\/sup><\/em><\/section>\n<section><\/section>\n<section>\u8bb8\u591a\u6570\u5b66\u5bb6\u91c7\u7528\u5965\u5361\u59c6\u5243\u5200\u89c2\u70b9\uff1a\u9664\u975e\u6709\u4ee4\u4eba\u4fe1\u670d\u7684\u7406\u7531\u8bf4\u660e\u4e00\u4e2a\u6570\u5e94\u8be5\u662f\u6709\u7406\u6570\uff0c\u5426\u5219\u5b83\u591a\u534a\u4e0d\u662f\u3002\u6bd5\u7adf\uff0c\u6570\u5b66\u5bb6\u4eec\u65e9\u5c31\u77e5\u9053\u5927\u591a\u6570\u6570\u90fd\u662f\u65e0\u7406\u6570\u3002<\/section>\n<section><\/section>\n<section>\u7136\u800c\uff0c\u51e0\u4e2a\u4e16\u7eaa\u4ee5\u6765\uff0c\u5177\u4f53\u6570\u7684\u65e0\u7406\u6027\u7684\u8bc1\u660e\u5374\u5f88\u5c11\u3002\u5728 18 \u4e16\u7eaa\uff0c\u6570\u5b66\u5de8\u4eba\u83b1\u6602\u54c8\u5fb7\u30fb\u6b27\u62c9\u8bc1\u660e\u4e86 e 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\u03b6(5)\u3002<\/section>\n<section><\/section>\n<section>\u6570\u5b66\u5bb6\u4eec\u4ecd\u5728\u653b\u575a\u5982\u6b64\u57fa\u672c\u7684\u6570\u95ee\u9898\uff0c\u8fd9\u53ef\u80fd\u770b\u8d77\u6765\u5f88\u4ee4\u4eba\u60ca\u8bb6\u3002\u4f46\u5373\u4f7f\u6709\u7406\u6027\u662f\u4e00\u4e2a\u57fa\u672c\u6982\u5ff5\uff0c\u7814\u7a76\u8005\u76ee\u524d\u4e5f\u53ea\u6709\u5f88\u5c11\u7684\u5de5\u5177\u53ef\u4ee5\u8bc1\u660e\u7ed9\u5b9a\u6570\u662f\u65e0\u7406\u6570\u3002\u800c\u4e14\u8fd9\u4e9b\u5de5\u5177\u7ecf\u5e38\u5931\u6548\u3002<\/section>\n<section><\/section>\n<section>\u5f53\u6570\u5b66\u5bb6\u6210\u529f\u8bc1\u660e\u4e00\u4e2a\u6570\u7684\u65e0\u7406\u6027\u65f6\uff0c\u4ed6\u4eec\u7684\u8bc1\u660e\u6838\u5fc3\u901a\u5e38\u4f9d\u8d56\u4e8e\u6709\u7406\u6570\u7684\u4e00\u4e2a\u57fa\u672c\u6027\u8d28\uff1a\u5b83\u4eec\u4e0d\u559c\u6b22\u5f7c\u6b64\u9760\u5f97\u592a\u8fd1\u3002\u4f8b\u5982\uff0c\u5047\u8bbe\u4f60\u9009\u62e9\u4e24\u4e2a\u5206\u6570\uff0c\u4e00\u4e2a\u5206\u6bcd\u662f 7\uff0c\u53e6\u4e00\u4e2a\u5206\u6bcd\u662f 100\u3002\u8981\u6d4b\u91cf\u5b83\u4eec\u4e4b\u95f4\u7684\u8ddd\u79bb\uff08\u7528\u8f83\u5927\u7684\u5206\u6570\u4e2d\u51cf\u53bb\u8f83\u5c0f\u7684\u5206\u6570\uff09\uff0c\u4f60\u5fc5\u987b\u91cd\u5199\u4f60\u7684\u5206\u6570\uff0c\u4f7f\u5b83\u4eec\u6709\u76f8\u540c\u7684\u5206\u6bcd\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u516c\u5171\u5206\u6bcd\u662f 700\u3002\u6240\u4ee5\u65e0\u8bba\u4f60\u4ece\u54ea\u4e24\u4e2a\u5206\u6570\u5f00\u59cb\uff0c\u5b83\u4eec\u4e4b\u95f4\u7684\u8ddd\u79bb\u90fd\u662f\u67d0\u4e2a\u6574\u6570\u9664\u4ee5 700\u2014\u2014 \u8fd9\u610f\u5473\u7740\u8fd9\u4e9b\u5206\u6570\u81f3\u5c11\u5fc5\u987b\u76f8\u8ddd 1\/700\u3002\u5982\u679c\u4f60\u60f3\u8981\u66f4\u76f8\u8fd1\u7684\u5206\u6570\uff0c\u4f60\u5c31\u5fc5\u987b\u589e\u5927\u5176\u4e2d\u4e00\u4e2a\u5206\u6570\u7684\u539f\u59cb\u5206\u6bcd\u3002<\/section>\n<section><\/section>\n<section>\u5c06\u8fd9\u79cd\u63a8\u7406\u7ffb\u8f6c\u8fc7\u6765\uff0c\u5b83\u5c31\u53d8\u6210\u4e86\u8bc1\u660e\u65e0\u7406\u6027\u7684\u6807\u51c6\u3002\u5047\u8bbe\u4f60\u6709\u4e00\u4e2a\u6570 k\uff0c\u4f60\u60f3\u5f04\u6e05\u695a\u5b83\u662f\u5426\u662f\u6709\u7406\u6570\u3002\u4e5f\u8bb8\u4f60\u6ce8\u610f\u5230 k \u548c 4\/7 \u4e4b\u95f4\u7684\u8ddd\u79bb\u5c0f\u4e8e 1\/700\u3002\u8fd9\u610f\u5473\u7740 k \u5982\u679c\u6709\u5206\u6bcd\uff0c\u5219\u5fc5\u4e0d\u53ef\u80fd\u662f 100 \u6216\u66f4\u5c0f\u7684\u6570\u3002\u63a5\u4e0b\u6765\uff0c\u4e5f\u8bb8\u4f60\u627e\u5230\u4e00\u4e2a\u65b0\u7684\u5206\u6570\uff0c\u8ba9\u4f60\u6392\u9664 k \u6709 1000 \u6216\u66f4\u5c0f\u5206\u6bcd\u7684\u53ef\u80fd\u6027 \u2014\u2014 \u7136\u540e\u53e6\u4e00\u4e2a\u5206\u6570\u6392\u9664 10,000 \u6216\u66f4\u5c0f\u7684\u5206\u6bcd\uff0c\u4ee5\u6b64\u7c7b\u63a8\u3002\u5982\u679c\u4f60\u80fd\u6784\u9020\u4e00\u4e2a\u65e0\u9650\u5e8f\u5217\u7684\u5206\u6570\uff0c\u9010\u6e10\u6392\u9664 k \u7684\u6bcf\u4e2a\u53ef\u80fd\u7684\u5206\u6bcd\uff0c\u90a3\u4e48 k \u5c31\u4e0d\u53ef\u80fd\u662f\u6709\u7406\u6570\u3002<\/section>\n<section><\/section>\n<section>\u51e0\u4e4e\u6bcf\u4e2a\u65e0\u7406\u6027\u8bc1\u660e\u90fd\u9075\u5faa\u8fd9\u4e9b\u601d\u8def\u3002\u4f46\u4f60\u4e0d\u80fd\u4ec5\u4ec5\u53d6\u4efb\u4f55\u63a5\u8fd1 k \u7684\u5206\u6570\u5e8f\u5217 \u2014\u2014 \u4f60\u9700\u8981\u6bd4\u5b83\u4eec\u7684\u5206\u6bcd\u66f4\u5feb\u63a5\u8fd1 k \u7684\u5206\u6570\u3002\u8fd9\u4fdd\u8bc1\u4e86\u5b83\u4eec\u6392\u9664\u7684\u5206\u6bcd\u4f1a\u6301\u7eed\u589e\u5927\u3002\u5982\u679c\u4f60\u7684\u5e8f\u5217\u63a5\u8fd1 k \u7684\u901f\u5ea6\u4e0d\u591f\u5feb\uff0c\u4f60\u53ea\u80fd\u6392\u9664\u5230\u67d0\u4e2a\u70b9\u7684\u5206\u6bcd\uff0c\u800c\u4e0d\u662f\u6240\u6709\u53ef\u80fd\u7684\u5206\u6bcd\u3002<\/section>\n<section><\/section>\n<section>\u76ee\u524d\u8fd8\u6ca1\u6709\u4e00\u79cd\u6784\u9020\u5408\u9002\u7684\u5206\u6570\u5e8f\u5217\u7684\u901a\u7528\u65b9\u6cd5\u3002\u6709\u65f6\u5019\uff0c\u4e00\u4e2a\u597d\u7684\u5e8f\u5217\u4f1a\u81ea\u7136\u51fa\u73b0\u3002\u4f8b\u5982\uff0c\u6570 e\uff08\u7ea6\u4e3a 2.71828\uff09\u7b49\u4e8e\u4ee5\u4e0b\u65e0\u9650\u548c\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-8c7ed297cdec3101d417895f3f390b62.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-8c7ed297cdec3101d417895f3f390b62.png\"><\/a><\/section>\n<section>\u5982\u679c\u4f60\u5728\u4efb\u4f55\u6709\u9650\u70b9\u505c\u6b62\u8fd9\u4e2a\u548c\u5e76\u52a0\u4e0a\u6240\u6709\u9879\uff0c\u4f60\u5f97\u5230\u7684\u662f\u4e00\u4e2a\u5206\u6570\u3002\u800c\u4e14\u53ea\u9700\u8981\u9ad8\u4e2d\u6570\u5b66\u5c31\u80fd\u8bc1\u660e\u8fd9\u4e2a\u5206\u6570\u5e8f\u5217\u63a5\u8fd1 e \u7684\u901f\u5ea6\u8db3\u591f\u5feb\uff0c\u53ef\u4ee5\u6392\u9664\u6240\u6709\u53ef\u80fd\u7684\u5206\u6bcd\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-a3fa1239f4fb7274e17259eb17da1cd1.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-a3fa1239f4fb7274e17259eb17da1cd1.png\"><\/a><\/section>\n<section><em><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Vesselin Dimitrov\uff0c\u4ed6\u4e0e\u5408\u4f5c\u8005\u7528\u4e86\u591a\u5e74\u65f6\u95f4\u6765\u8bc1\u660e L (2) \u7684\u65e0\u7406\u6027\uff0c\u6700\u7ec8\u89e3\u51b3\u4e86\u6570\u8bba\u4e2d\u4e00\u4e2a\u91cd\u8981\u7684\u3001\u770b\u4f3c\u4e0d\u76f8\u5173\u7684\u731c\u60f3\u3002<\/sup><\/em><\/section>\n<section><\/section>\n<section>\u4f46\u8fd9\u4e2a\u6280\u5de7\u5e76\u4e0d\u603b\u662f\u6709\u6548\u3002\u5982\uff0c\u963f\u57f9\u91cc\u7684\u65e0\u7406\u6570 \u03b6(3) \u88ab\u5b9a\u4e49\u4e3a\u8fd9\u4e2a\u65e0\u9650\u548c\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-df8e3684a3a0897c132e39844d553474.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-df8e3684a3a0897c132e39844d553474.png\"><\/a><\/section>\n<section>\u5982\u679c\u4f60\u5728\u6bcf\u4e2a\u6709\u9650\u6b65\u9aa4\u505c\u6b62\u8fd9\u4e2a\u548c\u5e76\u52a0\u4e0a\u6240\u6709\u9879\uff0c\u5f97\u5230\u7684\u5206\u6570\u63a5\u8fd1 \u03b6(3) \u7684\u901f\u5ea6\u4e0d\u591f\u5feb\uff0c\u4e0d\u80fd\u6392\u9664 \u03b6(3) \u7684\u6bcf\u4e2a\u53ef\u80fd\u7684\u5206\u6bcd\u3002\u03b6(3) \u53ef\u80fd\u662f\u4e00\u4e2a\u5206\u6bcd\u6bd4\u4f60\u5df2\u7ecf\u6392\u9664\u7684\u66f4\u5927\u7684\u6709\u7406\u6570\u3002<\/section>\n<section><\/section>\n<section>\u963f\u57f9\u91cc\u7684\u5929\u624d\u4e4b\u5904\u5728\u4e8e\u6784\u9020\u4e86\u4e00\u4e2a\u4e0d\u540c\u7684\u5206\u6570\u5e8f\u5217\uff0c\u8fd9\u4e2a\u5e8f\u5217\u786e\u5b9e\u8db3\u591f\u5feb\u5730\u63a5\u8fd1 \u03b6(3)\uff0c\u53ef\u4ee5\u6392\u9664\u6bcf\u4e2a\u5206\u6bcd\u3002\u4ed6\u7684\u6784\u9020\u4f7f\u7528\u4e86\u53ef\u4ee5\u8ffd\u6eaf\u5230\u51e0\u4e2a\u4e16\u7eaa\u524d\u7684\u6570\u5b66 \u2014\u2014 \u4e00\u7bc7\u6587\u7ae0\u79f0\u4e4b\u4e3a\u300c\u6b27\u62c9\u9519\u8fc7\u7684\u8bc1\u660e\u300d\u3002\u4f46\u5373\u4f7f\u5728\u6570\u5b66\u5bb6\u7406\u89e3\u4e86\u4ed6\u7684\u65b9\u6cd5\u4e4b\u540e\uff0c\u4ed6\u4eec\u4e5f\u65e0\u6cd5\u5c06\u4ed6\u7684\u6210\u529f\u6269\u5c55\u7528\u4e8e\u5176\u4ed6\u76f8\u5173\u7684\u6570\u3002<\/section>\n<section><\/section>\n<section>\u50cf\u6bcf\u4e2a\u65e0\u7406\u6027\u8bc1\u660e\u4e00\u6837\uff0c\u963f\u57f9\u91cc\u7684\u7ed3\u679c\u7acb\u5373\u610f\u5473\u7740\u8bb8\u591a\u5176\u4ed6\u6570\u4e5f\u662f\u65e0\u7406\u6570\uff0c\u4f8b\u5982\uff0c\u03b6(3) + 3\uff0c\u6216 4 \u00d7 \u03b6(3)\u3002\u4f46\u6570\u5b66\u5bb6\u4eec\u5bf9\u8fd9\u79cd\u514d\u8d39\u5f97\u5230\u7684\u7ed3\u679c\u4e0d\u4f1a\u592a\u5174\u594b\u3002\u4ed6\u4eec\u771f\u6b63\u60f3\u8981\u7684\u662f\u8bc1\u660e\u300c\u91cd\u8981\u300d\u7684\u6570\u662f\u65e0\u7406\u6570 \u2014\u2014 \u90a3\u4e9b\u300c\u5728\u4e00\u4e2a\u516c\u5f0f\u4e2d\u51fa\u73b0\uff0c[\u7136\u540e] \u5728\u53e6\u4e00\u4e2a\u516c\u5f0f\u4e2d\u51fa\u73b0\uff0c\u4e5f\u5728\u6570\u5b66\u7684\u4e0d\u540c\u90e8\u5206\u51fa\u73b0\u300d\u7684\u6570\uff0cZudilin \u8bf4\u3002<\/section>\n<section><\/section>\n<section>\u9ece\u66fc zeta \u51fd\u6570\u548c\u76f8\u5173\u7684 L &#8211; \u51fd\u6570\u7684\u503c\u975e\u5e38\u6ee1\u8db3\u8fd9\u4e2a\u6807\u51c6\uff0c\u5f88\u5c11\u6709\u6570\u80fd\u6bd4\u5b83\u4eec\u66f4\u52a0\u6ee1\u8db3\u3002\u9ece\u66fc zeta \u51fd\u6570 \u03b6(x) \u4f1a\u5c06\u4e00\u4e2a\u6570 x \u8f6c\u6362\u4e3a\u8fd9\u4e2a\u65e0\u9650\u548c\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-75dddb50cd73054c00fade2c410719cb.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-75dddb50cd73054c00fade2c410719cb.png\"><\/a><\/section>\n<section>\u4e3e\u4e2a\u4f8b\u5b50\uff0c\u03b6(3) \u5c31\u662f\u5f53\u4f60\u4ee3\u5165 x = 3 \u65f6\u5f97\u5230\u7684\u65e0\u9650\u548c\u3002\u957f\u671f\u4ee5\u6765\uff0c\u5f88\u591a\u4eba\u90fd\u8ba4\u4e3a zeta \u51fd\u6570\u652f\u914d\u7740\u7d20\u6570\u7684\u5206\u5e03\u3002\u540c\u65f6\uff0cL &#8211; \u51fd\u6570 \u2014\u2014 \u5b83\u4eec\u50cf zeta \u51fd\u6570\u4f46\u6709\u4e0d\u540c\u7684\u5206\u5b50 \u2014\u2014 \u652f\u914d\u7740\u66f4\u590d\u6742\u6570\u7cfb\u4e2d\u7d20\u6570\u7684\u5206\u5e03\u3002\u5728\u8fc7\u53bb 50 \u5e74\u91cc\uff0cL &#8211; \u51fd\u6570\u5728\u6570\u8bba\u4e2d\u56e0\u5176\u5728\u6717\u5170\u5179\u7eb2\u9886\u4e2d\u7684\u5173\u952e\u4f5c\u7528\u800c\u53d8\u5f97\u7279\u522b\u7a81\u51fa\uff0c\u6717\u5170\u5179\u7eb2\u9886\u662f\u6784\u5efa\u6570\u5b66\u300c\u5927\u7edf\u4e00\u7406\u8bba\u300d\u7684\u96c4\u5fc3\u52c3\u52c3\u7684\u52aa\u529b\u3002\u4f46\u5b83\u4eec\u4e5f\u51fa\u73b0\u5728\u6570\u5b66\u4e2d\u5176\u5b83\u5b8c\u5168\u4e0d\u540c\u7684\u9886\u57df\u3002\u4f8b\u5982\uff0c\u53d6\u4e00\u4e2a\u5206\u5b50\u9075\u5faa 1, -1, 0, 1, -1, 0 \u91cd\u590d\u6a21\u5f0f\u7684 L &#8211; \u51fd\u6570\uff0c\u4f1a\u5f97\u5230\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-bf5798b3de5aa957688b627880ec7665.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-bf5798b3de5aa957688b627880ec7665.png\"><\/a><\/section>\n<section>\u8fd9\u4e2a\u51fd\u6570\uff08\u4e0b\u9762\u6211\u4eec\u5c06\u5176\u5199\u6210 L (x)\uff09\u9664\u4e86\u5728\u6570\u8bba\u4e2d\u5927\u6709\u4f5c\u7528\uff0c\u5728\u51e0\u4f55\u5b66\u4e2d\u4e5f\u4f1a\u610f\u5916\u5730\u51fa\u73b0\u3002\u4f8b\u5982\uff0c\u5982\u679c\u4f60\u5c06 L (2) \u4e58\u4ee5\u4e00\u4e2a\u7b80\u5355\u7684\u56e0\u5b50\uff0c\u4f1a\u5f97\u5230\u5177\u6709\u300c\u53cc\u66f2\u300d\u51e0\u4f55\uff08\u9a6c\u978d\u5f62\u72b6\u7684\u5f2f\u66f2\u51e0\u4f55\uff09\u7684\u6700\u5927\u6b63\u56db\u9762\u4f53\u7684\u4f53\u79ef\u3002<\/section>\n<section><\/section>\n<section>\u6570\u5b66\u5bb6\u4eec\u81f3\u5c11\u7814\u7a76\u4e86 L (2) \u4e24\u4e2a\u4e16\u7eaa\u3002\u591a\u5e74\u6765\uff0c\u4ed6\u4eec\u60f3\u51fa\u4e86\u4e03\u516b\u79cd\u4e0d\u540c\u7684\u65b9\u6cd5\u7528\u6709\u7406\u6570\u5e8f\u5217\u6765\u903c\u8fd1\u5b83\u3002\u4f46\u8fd9\u4e9b\u5e8f\u5217\u90fd\u4e0d\u80fd\u8db3\u591f\u5feb\u5730\u63a5\u8fd1\u5b83\uff0c\u4e0d\u8db3\u4ee5\u8bc1\u660e\u5b83\u662f\u65e0\u7406\u6570\u3002<\/section>\n<section><\/section>\n<section>\u7814\u7a76\u8005\u4f3c\u4e4e\u9677\u5165\u4e86\u50f5\u5c40 \u2014\u2014 \u76f4\u5230 Calegari\u3001Dimitrov \u548c\u5510\u4e91\u6e05\u51b3\u5b9a\u5c06\u5176\u4f5c\u4e3a\u4ed6\u4eec\u65b0\u7684\u65e0\u7406\u6027\u65b9\u6cd5\u7684\u6838\u5fc3\u3002<\/section>\n<section><\/section>\n<section><strong>\u9ece\u66fc\u9519\u8fc7\u7684\u8bc1\u660e<\/strong><\/section>\n<section><\/section>\n<section>\u5728\u65e0\u7406\u6027\u8bc1\u660e\u4e2d\uff0c\u4f60\u5e0c\u671b\u4f60\u7684\u5206\u6570\u5e8f\u5217\u6392\u9664\u8d8a\u6765\u8d8a\u5927\u7684\u5206\u6bcd\u3002\u6570\u5b66\u5bb6\u4eec\u6709\u4e00\u4e2a\u5907\u53d7\u559c\u7231\u7684\u7b56\u7565\u6765\u7406\u89e3\u8fd9\u6837\u7684\u5e8f\u5217\uff1a\u4ed6\u4eec\u4f1a\u5c06\u5176\u6253\u5305\u6210\u4e00\u4e2a\u51fd\u6570\u3002\u901a\u8fc7\u7814\u7a76\u8fd9\u4e2a\u51fd\u6570\uff0c\u4ed6\u4eec\u83b7\u5f97\u4e86\u4e00\u7cfb\u5217\u5de5\u5177\uff0c\u5305\u62ec\u6240\u6709\u5fae\u79ef\u5206\u7684\u6280\u672f\u3002<\/section>\n<section><\/section>\n<section>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6570\u5b66\u5bb6\u4f1a\u6784\u9020\u4e00\u4e2a\u300c\u5e42\u7ea7\u6570\u300d\u2014\u2014 \u4e00\u4e2a\u5177\u6709\u65e0\u9650\u591a\u9879\u7684\u6570\u5b66\u8868\u8fbe\u5f0f\uff0c\u6bd4\u5982 3 + 2x + 7x\u00b2 + 4x\u00b3 + \u2026\u2014\u2014 \u5176\u4e2d\u6bcf\u4e2a\u7cfb\u6570\u90fd\u662f\u901a\u8fc7\u5c06\u4f60\u7814\u7a76\u7684\u6570\u4e0e\u5e8f\u5217\u4e2d\u7684\u4e00\u4e2a\u5206\u6570\u6309\u7167\u7279\u5b9a\u516c\u5f0f\u7ec4\u5408\u800c\u786e\u5b9a\u7684\u3002\u7b2c\u4e00\u4e2a\u7cfb\u6570\u6700\u7ec8\u6355\u6349\u5230\u7b2c\u4e00\u4e2a\u5206\u6570\u6392\u9664\u7684\u5206\u6bcd\u7684\u5927\u5c0f\uff1b\u7b2c\u4e8c\u4e2a\u7cfb\u6570\u6355\u6349\u5230\u7b2c\u4e8c\u4e2a\u5206\u6570\u6392\u9664\u7684\u5206\u6bcd\u7684\u5927\u5c0f\uff1b\u4f9d\u6b64\u7c7b\u63a8\u3002<\/section>\n<section><\/section>\n<section>\u7c97\u7565\u5730\u8bf4\uff0c\u7cfb\u6570\u548c\u88ab\u6392\u9664\u7684\u5206\u6bcd\u6709\u4e00\u4e2a\u53cd\u6bd4\u5173\u7cfb\uff0c\u8fd9\u610f\u5473\u7740\u4f60\u7684\u76ee\u6807 \u2014\u2014 \u8bc1\u660e\u88ab\u6392\u9664\u7684\u5206\u6bcd\u8d8b\u5411\u4e8e\u65e0\u7a77 \u2014\u2014 \u7b49\u4ef7\u4e8e\u8bc1\u660e\u7cfb\u6570\u8d8b\u5411\u4e8e\u96f6\u3002<\/section>\n<section><\/section>\n<section>\u8fd9\u79cd\u91cd\u65b0\u6253\u5305\u7684\u4f18\u52bf\u5728\u4e8e\u4f60\u53ef\u4ee5\u5c1d\u8bd5\u4f7f\u7528\u6574\u4e2a\u5e42\u7ea7\u6570\u7684\u6027\u8d28\u6765\u63a7\u5236\u7cfb\u6570\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4f60\u60f3\u7814\u7a76\u54ea\u4e9b x \u503c\u4f1a\u4f7f\u5e42\u7ea7\u6570\u300c\u7206\u70b8\u300d\u5230\u65e0\u7a77\u3002\u5e42\u7ea7\u6570\u4e2d\u7684\u9879\u6d89\u53ca x \u7684\u8d8a\u6765\u8d8a\u9ad8\u7684\u5e42\uff0c\u6240\u4ee5\u9664\u975e\u5b83\u4eec\u4e0e\u6781\u5c0f\u7684\u7cfb\u6570\u914d\u5bf9\uff0c\u5426\u5219\u5927\u7684 x \u503c\u4f1a\u4f7f\u5e42\u7ea7\u6570\u7206\u70b8\u3002\u56e0\u6b64\uff0c\u5982\u679c\u4f60\u80fd\u8bc1\u660e\u5e42\u7ea7\u6570\u5373\u4f7f\u5728\u5927\u7684 x \u503c\u4e0b\u4e5f\u4e0d\u4f1a\u7206\u70b8\uff0c\u8fd9\u5c31\u544a\u8bc9\u4f60\u7cfb\u6570\u786e\u5b9e\u4f1a\u6536\u7f29\u5230\u96f6\uff0c\u6b63\u5982\u4f60\u60f3\u8981\u7684\u90a3\u6837\u3002<\/section>\n<section><\/section>\n<section>\u4e3a\u4e86\u5f15\u5165\u7279\u522b\u4e30\u5bcc\u7684\u5de5\u5177\u96c6\u6765\u5904\u7406\u8fd9\u4e2a\u95ee\u9898\uff0c\u6570\u5b66\u5bb6\u8003\u8651 x \u7684\u300c\u590d\u6570\u300d\u503c\u3002\u590d\u6570\u7ed3\u5408\u4e86\u5b9e\u90e8\u548c\u865a\u90e8\uff0c\u53ef\u4ee5\u8868\u793a\u4e3a\u4e8c\u7ef4\u5e73\u9762\u4e2d\u7684\u70b9\u3002<\/section>\n<section><\/section>\n<section>\u60f3\u8c61\u5728\u590d\u6570\u5e73\u9762\u4e2d\u4ece\u96f6\u70b9\u5f00\u59cb\uff0c\u81a8\u80c0\u4e00\u4e2a\u5706\u76d8\uff0c\u76f4\u5230\u4f60\u78b0\u5230\u7b2c\u4e00\u4e2a\u4f7f\u4f60\u7684\u5e42\u7ea7\u6570\u7206\u70b8\u5230\u65e0\u7a77\u7684\u590d\u6570 \u2014\u2014 \u6570\u5b66\u5bb6\u79f0\u4e4b\u4e3a\u5947\u70b9\u3002\u5982\u679c\u8fd9\u4e2a\u5706\u76d8\u7684\u534a\u5f84\u8db3\u591f\u5927\uff0c\u4f60\u53ef\u4ee5\u63a8\u65ad\u5e42\u7ea7\u6570\u7684\u7cfb\u6570\u8db3\u591f\u5feb\u5730\u6536\u7f29\u5230\u96f6\uff0c\u4ece\u800c\u63a8\u51fa\u4f60\u7684\u6570\u662f\u65e0\u7406\u6570\u3002<\/section>\n<section><\/section>\n<section>\u963f\u57f9\u91cc\u7684\u8bc1\u660e\u548c\u8bb8\u591a\u5176\u4ed6\u65e0\u7406\u6027\u7ed3\u679c\u53ef\u4ee5\u7528\u8fd9\u4e9b\u672f\u8bed\u91cd\u65b0\u8868\u8ff0\uff0c\u5c3d\u7ba1\u5b83\u4eec\u6700\u521d\u5e76\u975e\u5982\u6b64\u5199\u6210\u3002\u4f46\u5bf9\u4e8e L (2) \u6765\u8bf4\uff0c\u5706\u76d8\u592a\u5c0f\u4e86\u3002\u5bf9\u8fd9\u4e2a\u6570\u5b57\uff0c\u6570\u5b66\u5bb6\u4eec\u8ba4\u4e3a\u5e42\u7ea7\u6570\u65b9\u6cd5\u662f\u6b7b\u8def\u4e00\u6761\u3002<\/section>\n<section><\/section>\n<section>\u4f46 Calegari\u3001Dimitrov \u548c\u5510\u4e91\u6e05\u770b\u5230\u4e86\u4e00\u4e2a\u6f5c\u5728\u7684\u7a81\u7834\u53e3\u3002\u5947\u70b9\u5e76\u4e0d\u603b\u662f\u4ee3\u8868\u6700\u7ec8\u7684\u505c\u6b62\u70b9 \u2014\u2014 \u8fd9\u53d6\u51b3\u4e8e\u5f53\u4f60\u78b0\u5230\u5947\u70b9\u65f6\u60c5\u51b5\u5982\u4f55\u3002\u6709\u65f6\u5706\u76d8\u7684\u8fb9\u754c\u4f1a\u78b0\u5230\u4e00\u5806\u5947\u70b9\u3002\u5982\u679c\u53d1\u751f\u8fd9\u79cd\u60c5\u51b5\uff0c\u4f60\u5c31\u5012\u9709\u4e86\u3002\u4f46\u5176\u4ed6\u65f6\u5019\uff0c\u8fb9\u754c\u4e0a\u53ef\u80fd\u53ea\u6709\u51e0\u4e2a\u5b64\u7acb\u7684\u5947\u70b9\u3002\u5728\u8fd9\u4e9b\u60c5\u51b5\u4e0b\uff0c\u4f60\u53ef\u80fd\u80fd\u591f\u5c06\u4f60\u7684\u5706\u76d8\u81a8\u80c0\u5230\u590d\u5e73\u9762\u7684\u66f4\u5927\u533a\u57df\uff0c\u907f\u5f00\u8fd9\u4e9b\u5947\u70b9\u3002<\/section>\n<section><\/section>\n<section>\u8fd9\u5c31\u662f Calegari\u3001Dimitrov \u548c\u5510\u4e91\u6e05\u5e0c\u671b\u505a\u7684\u3002\u4ed6\u4eec\u60f3\uff0c\u8fd9\u4e2a\u66f4\u5927\u533a\u57df\u4e2d\u5305\u542b\u7684\u989d\u5916\u4fe1\u606f\u53ef\u80fd\u4f7f\u4ed6\u4eec\u80fd\u591f\u5bf9\u5e42\u7ea7\u6570\u7684\u7cfb\u6570\u8fdb\u884c\u6240\u9700\u7684\u63a7\u5236\u3002\u4e00\u4e9b\u5e42\u7ea7\u6570\uff0cCalegari \u8bf4\uff0c\u53ef\u4ee5\u5728\u300c\u5706\u76d8\u4e4b\u5916\u8fc7\u7740\u7f8e\u597d\u7684\u751f\u6d3b\u300d\u3002<\/section>\n<section><\/section>\n<section>\u5728\u56db\u5e74\u7684\u65f6\u95f4\u91cc\uff0c\u8fd9\u51e0\u4f4d\u6570\u5b66\u5bb6\u5f04\u6e05\u695a\u4e86\u5982\u4f55\u4f7f\u7528\u8fd9\u79cd\u65b9\u6cd5\u6765\u8bc1\u660e L (2) \u662f\u65e0\u7406\u6570\u3002\u300c\u4ed6\u4eec\u5f00\u53d1\u4e86\u4e00\u4e2a\u5168\u65b0\u7684\u6807\u51c6\u6765\u51b3\u5b9a\u4e00\u4e2a\u7ed9\u5b9a\u7684\u6570\u5b57\u662f\u5426\u662f\u65e0\u7406\u6570\uff0c\u300dZudilin \u8bf4\u3002\u300c\u8fd9\u771f\u662f\u4ee4\u4eba\u60ca\u53f9\u3002\u300d<\/section>\n<section><\/section>\n<section>\u4e0e\u963f\u57f9\u91cc\u7684\u8bc1\u660e\u4e00\u6837\uff0c\u65b0\u65b9\u6cd5\u662f\u5bf9\u65e9\u671f\u65b9\u6cd5\u7684\u91cd\u65b0\u5229\u7528\uff0c\u4e25\u91cd\u4f9d\u8d56\u5bf9 19 \u4e16\u7eaa\u7684\u5fae\u79ef\u5206\u7684\u6cdb\u5316\u3002Bost \u751a\u81f3\u79f0\u65b0\u5de5\u4f5c\u4e3a\u300c\u9ece\u66fc\u9519\u8fc7\u7684\u8bc1\u660e\u300d\u3002\u8fd9\u91cc\u7684\u9ece\u66fc\u6307\u7684\u662f\u4f2f\u6069\u54c8\u5fb7\u30fb\u9ece\u66fc\uff0c\u4ed6\u662f 19 \u4e16\u7eaa\u6700\u6770\u51fa\u7684\u6570\u5b66\u5bb6\u4e4b\u4e00\uff0c\u9ece\u66fc zeta \u51fd\u6570\u5c31\u662f\u4ee5\u4ed6\u7684\u540d\u5b57\u547d\u540d\u7684\u3002\u9ece\u66fc\u7559\u7ed9\u540e\u4eba\u7684\u96be\u9898\u4e4b\u4e00\u5c31\u662f\u8457\u540d\u7684\u9ece\u66fc\u731c\u60f3\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-93ec4b5f8282e0608fc329a66012c886.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-93ec4b5f8282e0608fc329a66012c886.png\"><\/a><\/section>\n<section><em><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u9ece\u66fc<\/sup><\/em><\/section>\n<section><\/section>\n<section>\u65b0\u7684\u8bc1\u660e\u5e76\u4e0d\u6b62\u4e8e L (2)\u3002\u6211\u4eec\u5c06 \u03b6(2) \u7684\u5206\u5b50\u4e2d\u7684 1 \u66ff\u6362\u6210\u4e09\u4e2a\u91cd\u590d\u7684\u6570\uff1a1, -1, 0, 1, -1, 0 \u7b49\u7b49\u3002\u4f60\u53ef\u4ee5\u7528\u4e09\u4e2a\u91cd\u590d\u7684\u5206\u5b50\u5236\u4f5c\u65e0\u9650\u591a\u4e2a\u5176\u4ed6 \u03b6(2) \u53d8\u4f53 \u2014\u2014 \u4f8b\u5982\uff0c\u91cd\u590d\u6a21\u5f0f 1, 4, 10, 1, 4, 10\u2026\uff0c\u4ea7\u751f\u65e0\u9650\u7684\u548c\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-c0685e540275bcf2816701a8a766e184.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-c0685e540275bcf2816701a8a766e184.png\"><\/a><\/section>\n<section>\u7814\u7a76\u4eba\u5458\u8bc1\u660e\uff0c\u6bcf\u4e2a\u8fd9\u6837\u7684\u548c\u90fd\u662f\u65e0\u7406\u6570\uff08\u524d\u63d0\u662f\u5b83\u4e0d\u52a0\u5230\u96f6\uff09\u3002\u4ed6\u4eec\u8fd8\u4f7f\u7528\u4ed6\u4eec\u7684\u65b9\u6cd5\u8bc1\u660e\u4e86\u4e00\u7ec4\u5b8c\u5168\u4e0d\u540c\u7684\u6570\u7684\u65e0\u7406\u6027\uff0c\u8fd9\u4e9b\u6570\u7531\u5bf9\u6570\u7684\u4e58\u79ef\u6784\u6210\u3002Bost \u8bf4\uff0c\u8fd9\u6837\u7684\u6570\u4e4b\u524d\u662f\u300c\u5b8c\u5168\u65e0\u6cd5\u89e6\u53ca\u7684\u300d\u3002<\/section>\n<section><\/section>\n<section>\u7814\u7a76\u4eba\u5458\u9884\u8ba1\uff0c\u5177\u6709\u56db\u4e2a\u6570\u5b57\u91cd\u590d\u6a21\u5f0f\u7684 \u03b6(2) \u53d8\u4f53\u53ef\u80fd\u662f\u4e0b\u4e00\u4e2a\u3002\u4ed6\u4eec\u628a\u5e0c\u671b\u5bc4\u6258\u5728\u8bc1\u660e\u300c\u5361\u5854\u5170\u5e38\u6570 (Catalan&#8217;s Constant)\u300d\u7684\u65e0\u7406\u6027\u4e0a \u2014\u2014 \u8fd9\u662f\u4e00\u4e2a\u5177\u6709\u91cd\u590d\u6a21\u5f0f 1, 0, -1, 0, 1, 0, -1, 0\u2026 \u7684\u53d8\u4f53\uff0c\u5df2\u7ecf\u88ab\u7814\u7a76\u4e86 150 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