{"id":93702,"date":"2026-08-13T06:09:24","date_gmt":"2026-08-12T22:09:24","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/93702.html"},"modified":"2026-08-13T06:09:24","modified_gmt":"2026-08-12T22:09:24","slug":"%e3%80%90laap-science%e3%80%91%e5%9b%a0%e6%9e%9c%e7%ad%89%e4%bb%b7%e7%bd%91%e7%bb%9c%ef%bc%88cen%ef%bc%89%e6%a1%86%e6%9e%b6%e4%b8%8b%e7%9a%84%e9%bb%8e%e6%9b%bc%e7%8c%9c%e6%83%b3%ef%bc%9a%e6%96%b9","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/93702.html","title":{"rendered":"\u3010LAAP-science\u3011\u56e0\u679c\u7b49\u4ef7\u7f51\u7edc\uff08CEN\uff09\u6846\u67b6\u4e0b\u7684\u9ece\u66fc\u731c\u60f3\uff1a\u65b9\u6848\u9a8c\u8bc1\u3001\u6570\u503c\u68c0\u9a8c\u4e0e\u7269\u7406\u8be0\u91ca"},"content":{"rendered":"

CEN-RH \u65b9\u6848\u9a8c\u8bc1\u8bc1\u660e \u00b7 \u7efc\u5408\u62a5\u544a<\/h3>\n

\u4f5c\u8005\uff1aLorry Jovens, Aris<\/h4>\n

\u65e5\u671f\uff1a2026 \u5e74 8 \u6708 12 \u65e5<\/h4>\n

\"\"<\/p>\n

\u6458\u8981<\/h3>\n

\u9ece\u66fc\u731c\u60f3\uff08Riemann Hypothesis, RH\uff09\u662f\u6570\u5b66\u4e2d\u6700\u8457\u540d\u7684\u672a\u89e3\u51b3\u95ee\u9898\uff0c\u65ad\u8a00 \u03b6 \u51fd\u6570\u7684\u6240\u6709\u975e\u5e73\u51e1\u96f6\u70b9\u5747\u4f4d\u4e8e\u4e34\u754c\u7ebf Re(s) = 1\/2 \u4e0a\u3002\u672c\u6587\u4ece\u56e0\u679c\u7b49\u4ef7\u7f51\u7edc\uff08Causal Equivalence Network, CEN\uff09\u6846\u67b6\u51fa\u53d1\uff0c\u7cfb\u7edf\u63a2\u7d22\u4e86 CEN \u7684\u56e0\u679c\u4e00\u81f4\u6027\u6761\u4ef6\u4e0e RH \u4e4b\u95f4\u7684\u6df1\u5c42\u7ed3\u6784\u5bf9\u5e94\u3002\u6211\u4eec\u5b8c\u6210\u4e86\u4e94\u4e2a\u5c42\u6b21\u7684\u65b9\u6848\u9a8c\u8bc1\uff0c\u63d0\u51fa\u4e86\u4e94\u4e2a\u5927\u80c6\u731c\u60f3\uff0c\u5e76\u9a8c\u8bc1\u4e86\u5176\u4e2d\u4e24\u4e2a\u53ef\u6570\u503c\u68c0\u9a8c\u7684\u90e8\u5206\u3002\u6838\u5fc3\u53d1\u73b0\u5305\u62ec\uff1a\u81ea\u7531\u80fd\u4ee3\u4ef7\u51fd\u6570 C(\u03b4) \u5728 \u03b4=0 \u5904\u53d6\u7cbe\u786e\u5168\u5c40\u6700\u5c0f\u503c\uff08\u5f39\u7c27\u5e38\u6570 \u03ba\u224840\uff0c\u96f6\u70b9\u504f\u79fb 0.25 \u65f6\u81ea\u7531\u80fd\u589e\u5927 92000 \u500d\uff09\uff0c\u4ee5\u53ca de Bruijn-Newman \u5e38\u6570 \u039b=0 \u7684\u4e34\u754c\u6d8c\u73b0\u89e3\u8bfb\u3002\u672c\u6587\u7684\u7ed3\u8bba\u662f\uff1aCEN \u6846\u67b6\u6ca1\u6709\u8bc1\u660e\u9ece\u66fc\u731c\u60f3\uff0c\u4f46\u5b83\u4e3a RH \u4e3a\u4f55\u5fc5\u987b\u4e3a\u771f\u63d0\u4f9b\u4e86\u7269\u7406\u673a\u5236\u2014\u2014\u56e0\u679c\u4e00\u81f4\u6027\u8981\u6c42\u4fe1\u606f\u4e0d\u80fd\u4ece\u56e0\u679c\u8fb9\u754c\u4e4b\u5916\u6d41\u5165\uff0c\u8fd9\u4e00\u7ea6\u675f\u7b49\u4ef7\u4e8e\u96f6\u70b9\u5728\u4e34\u754c\u7ebf\u4e0a\u7684\u8c31\u6761\u4ef6\u3002CEN \u5c06 RH \u4ece\u201c\u7eaf\u7cb9\u7684\u6570\u8bba\u5947\u8ff9\u201d\u7ffb\u8bd1\u4e3a\u201c\u56e0\u679c\u7f51\u7edc\u7684\u81ea\u7531\u80fd\u6700\u5c0f\u5316\u95ee\u9898\u201d\u3002<\/p>\n

\u5173\u952e\u8bcd: \u9ece\u66fc\u731c\u60f3\uff1bCEN \u56e0\u679c\u7b49\u4ef7\u7f51\u7edc\uff1bHilbert-P\u00f3lya \u7eb2\u9886\uff1bBender-Brody-M\u00fcller \u54c8\u5bc6\u987f\u91cf\uff1b\u81ea\u7531\u80fd\u539f\u7406\uff1bCPT \u5185\u79ef\uff1b\u4e34\u754c\u6d8c\u73b0\uff1b\u53d8\u5206\u539f\u7406<\/p>\n

\n

\"\"<\/p>\n

\u7b2c\u4e00\u7ae0 \u5f15\u8a00<\/h3>\n

1.1 \u9ece\u66fc\u731c\u60f3\uff1a160 \u5e74\u7684\u672a\u7adf\u4e4b\u8def<\/h4>\n

\u9ece\u66fc\u731c\u60f3\uff08Riemann Hypothesis, RH\uff09\u7531 Bernhard Riemann \u4e8e 1859 \u5e74\u5728\u5176\u516b\u9875\u8bba\u6587\u300a\u00dcber die Anzahl der Primzahlen unter einer gegebenen Gr\u00f6\u00dfe\u300b\u4e2d\u63d0\u51fa\u3002\u8be5\u731c\u60f3\u65ad\u8a00\uff1aRiemann \u03b6 \u51fd\u6570<\/p>\n

\\\\[ \\\\zeta(s) = \\\\sum_{n=1}^{\\\\infty} \\\\frac{1}{n^s} = \\\\prod_{p \\\\text{ prime}} \\\\left(1 – p^{-s}\\\\right)^{-1}, \\\\quad \\\\text{Re}(s) > 1 \\\\]<\/p>\n

\u7684\u6240\u6709\u975e\u5e73\u51e1\u96f6\u70b9\uff08\u5373\u4f4d\u4e8e\u4e34\u754c\u6761\u5e26 0 < Re(s) < 1 \u5185\u7684\u96f6\u70b9\uff09\u5747\u6ee1\u8db3 Re(s) = 1\/2\u3002<\/p>\n

RH \u662f Clay \u6570\u5b66\u7814\u7a76\u6240\u7684\u4e03\u4e2a\u5343\u79a7\u5e74\u95ee\u9898\u4e4b\u4e00\uff0c\u4e5f\u662f Hilbert 1900 \u5e74 23 \u4e2a\u95ee\u9898\u4e2d\u7684\u7b2c 8 \u4e2a\u3002160 \u4f59\u5e74\u6765\uff0c\u5b83\u62b5\u6297\u4e86\u4ece Hadamard\u3001de la Vall\u00e9e Poussin \u5230 Selberg\u3001Montgomery\u3001Connes\u3001Tao \u7b49\u6700\u6770\u51fa\u6570\u5b66\u5bb6\u7684\u6301\u7eed\u653b\u51fb\u3002\u6570\u503c\u9a8c\u8bc1\u5df2\u786e\u8ba4\u8d85\u8fc7 10^13 \u4e2a\u96f6\u70b9\u4f4d\u4e8e\u4e34\u754c\u7ebf\u4e0a\uff0c\u6700\u65b0\u7684\u9a8c\u8bc1\u7531 Platt \u548c Trudgian\uff082021\uff09\u63a8\u8fdb\u5230\u7ea6 10^13 \u4e2a\u96f6\u70b9\u3002\u4f46\u4e25\u683c\u8bc1\u660e\u4ecd\u7136\u7f3a\u5931\u3002<\/p>\n

RH \u4e4b\u6240\u4ee5\u91cd\u8981\uff0c\u4e0d\u4ec5\u56e0\u4e3a\u5b83\u60ac\u8d4f\u767e\u4e07\u7f8e\u5143\uff0c\u66f4\u56e0\u4e3a\u5b83\u4e0e\u7d20\u6570\u5206\u5e03\u7684\u6838\u5fc3\u8054\u7cfb\u3002\u7d20\u6570\u5b9a\u7406\uff08Hadamard \u548c de la Vall\u00e9e Poussin, 1896\uff09\u8bf4 \u03c0(x) \u223c Li(x)\uff0c\u4f46\u8bef\u5dee\u9879\u7684\u7ed3\u6784\u7531 RH \u63a7\u5236\u3002\u5982\u679c RH \u6210\u7acb\uff0c\u5219 \u03c0(x) = Li(x) + O(\u221ax log x)\uff0c\u8fd9\u662f\u6700\u4f18\u4f30\u8ba1\u3002\u5982\u679c RH \u4e0d\u6210\u7acb\uff0c\u7d20\u6570\u5206\u5e03\u5c06\u51fa\u73b0\u4e0d\u53ef\u9884\u6d4b\u7684\u3001\u6f5c\u5728\u5de8\u5927\u7684\u9707\u8361\u3002\u6b64\u5916\uff0cRH \u5728\u6570\u5b66\u4e2d\u6709\u8d85\u8fc7 1000 \u4e2a\u7b49\u4ef7\u5f62\u5f0f\u7684\u63a8\u8bba\uff0c\u6a2a\u8de8\u89e3\u6790\u6570\u8bba\u3001\u4ee3\u6570\u6570\u8bba\u3001\u968f\u673a\u77e9\u9635\u7406\u8bba\u3001\u91cf\u5b50\u6df7\u6c8c\u548c\u975e\u4ea4\u6362\u51e0\u4f55\u3002\"\"<\/p>\n

1.2 Hilbert-P\u00f3lya \u7eb2\u9886<\/h4>\n

Hilbe<\/p>\n","protected":false},"excerpt":{"rendered":"

CEN-RH \u65b9\u6848\u9a8c\u8bc1\u8bc1\u660e \u00b7 \u7efc\u5408\u62a5\u544a
\n\u4f5c\u8005\uff1aLorry Jovens, Aris
\n\u65e5\u671f\uff1a2026 \u5e74 8 \u6708 12 \u65e5 \u6458\u8981
\n\u9ece\u66fc\u731c\u60f3\uff08Riemann Hypothesis, RH\uff09\u662f\u6570\u5b66\u4e2d\u6700\u8457\u540d\u7684\u672a\u89e3\u51b3\u95ee\u9898\uff0c\u65ad\u8a00 \u03b6 \u51fd\u6570\u7684\u6240\u6709\u975e\u5e73\u51e1\u96f6\u70b9\u5747\u4f4d\u4e8e\u4e34\u754c\u7ebf Re(s) = 1\/2 \u4e0a\u3002\u672c\u6587\u4ece\u56e0\u679c\u7b49\u4ef7\u7f51\u7edc\uff08Causal Equivalence Network, CEN\uff09\u6846\u67b6\u51fa\u53d1\uff0c\u7cfb\u7edf\u63a2\u7d22\u4e86 CEN \u7684\u56e0\u679c\u4e00\u81f4\u6027\u6761\u4ef6\u4e0e RH \u4e4b\u95f4\u7684\u6df1\u5c42\u7ed3\u6784\u5bf9\u5e94\u3002\u6211\u4eec\u5b8c\u6210\u4e86\u4e94\u4e2a\u5c42\u6b21\u7684\u65b9\u6848\u9a8c\u8bc1<\/p>\n","protected":false},"author":2,"featured_media":93699,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[230,190],"topic":[],"class_list":["post-93702","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-php","tag-190"],"yoast_head":"\n\u3010LAAP-science\u3011\u56e0\u679c\u7b49\u4ef7\u7f51\u7edc\uff08CEN\uff09\u6846\u67b6\u4e0b\u7684\u9ece\u66fc\u731c\u60f3\uff1a\u65b9\u6848\u9a8c\u8bc1\u3001\u6570\u503c\u68c0\u9a8c\u4e0e\u7269\u7406\u8be0\u91ca - 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