{"id":65508,"date":"2025-12-16T22:43:06","date_gmt":"2025-12-16T13:43:06","guid":{"rendered":"https:\/\/wordpress.realcollector.jp\/blog\/?p=65508"},"modified":"2025-12-16T22:43:06","modified_gmt":"2025-12-16T13:43:06","slug":"zeta","status":"publish","type":"post","link":"https:\/\/wordpress.realcollector.jp\/blog\/?p=65508","title":{"rendered":"zeta"},"content":{"rendered":"<p>\u4ee5\u4e0b\u3067\u306f\u300c\u30ea\u30fc\u30de\u30f3\u30bc\u30fc\u30bf\u95a2\u6570\uff08Riemann \u03b6 \u95a2\u6570\uff09\u300d\u306b\u3064\u3044\u3066\u3001500\u8a9e\u4ee5\u4e0a\u306e\u65e5\u672c\u8a9e\u306b\u3088\u308b\u89e3\u8aac\u3092\u884c\u3044\u3001\u305d\u306e\u5f8c\u7279\u5fb4\u3092\u7b87\u6761\u66f8\u304d\u3067\u3001\u3055\u3089\u306b\u53c2\u8003\u6587\u732e\u30fb\u53c2\u8003\u30b5\u30a4\u30c8\u30925\u4ef6\u4ee5\u4e0a\u6319\u3052\u307e\u3059\u3002<\/p>\n<p>\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \uff11\uff0e\u30ea\u30fc\u30de\u30f3\u30bc\u30fc\u30bf\u95a2\u6570\u3068\u306f\u4f55\u304b\uff1f \u30ea\u30fc\u30de\u30f3\u30bc\u30fc\u30bf\u95a2\u6570 \u03b6(s) \u306f\u3001\u8907\u7d20\u6570 s \u3092\u5909\u6570\u3068\u3059\u308b\u7279\u6b8a\u95a2\u6570\u306e\u4e00\u3064\u3067\u3059\u3002\u30aa\u30a4\u30e9\u30fc\uff08Leonhard Euler\uff09\u304c\u8003\u6848\u3057\u305f\u7d1a\u6570 \u3000\u3000\u03b6(s) = \u03a3_{n=1}^\u221e 1 \/ n^s \u3092\u8d77\u6e90\u3068\u3057\u3001\u30d9\u30eb\u30f3\u30cf\u30eb\u30c8\u30fb\u30ea\u30fc\u30de\u30f3\uff08Bernhard Riemann\uff09\u304c\u89e3\u6790\u63a5\u7d9a\u3084\u95a2\u6570\u7b49\u5f0f\u3092\u5c0e\u5165\u3059\u308b\u3053\u3068\u3067\u4e00\u822c\u7684\u306a\u8907\u7d20\u89e3\u6790\u306e\u67a0\u7d44\u307f\u306b\u7d44\u307f\u8fbc\u307f\u307e\u3057\u305f\u3002\u5b9f\u90e8 Re(s) &gt; 1 \u3067\u7d1a\u6570\u304c\u7d76\u5bfe\u53ce\u675f\u3057\u3001\u305d\u308c\u4ee5\u5916\u306e s \u306b\u3082\u89e3\u6790\u63a5\u7d9a\u306b\u3088\u308a\u6709\u610f\u7fa9\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002 \u6570\u8ad6\u306b\u304a\u3044\u3066\u306f\u7d20\u6570\u5206\u5e03\u3068\u306e\u6df1\u3044\u95a2\u4fc2\u3092\u6301\u3061\u3001\u7279\u306b\u300c\u30ea\u30fc\u30de\u30f3\u4e88\u60f3\u300d\u3068\u547c\u3070\u308c\u308b\u672a\u89e3\u6c7a\u554f\u984c\u306f \u03b6(s) \u306e\u975e\u81ea\u660e\u306a\u96f6\u70b9\u304c\u5b9f\u90e8 1\/2 \u4e0a\u306b\u5168\u3066\u5b58\u5728\u3059\u308b\u3068\u3059\u308b\u6709\u540d\u306a\u4eee\u8aac\u3067\u3059\u3002 \u307e\u305f\u7269\u7406\u5b66\u306e\u7d71\u8a08\u529b\u5b66\u3084\u91cf\u5b50\u5834\u7406\u8ad6\u306b\u304a\u3044\u3066\u3082\u3001\u30bc\u30fc\u30bf\u6a5f\u80fd\u306e\u6b63\u5247\u5316\u624b\u6cd5\uff08\u03b6-\u95a2\u6570\u6b63\u5247\u5316\uff09\u304c\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u7121\u9650\u767a\u6563\u3092\u6271\u3046\u969b\u306b\u7528\u3044\u3089\u308c\u308b\u306a\u3069\u3001\u7406\u8ad6\u7269\u7406\u3078\u306e\u5fdc\u7528\u3082\u5e83\u304f\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\uff12\uff0e\u6b74\u53f2\u7684\u80cc\u666f \u30fb18\u4e16\u7d00\u5f8c\u534a\uff1a\u30aa\u30a4\u30e9\u30fc\u304c\u5b9f\u6570 s \u306b\u5bfe\u3057 \u03a3 1\/n^s \u3092\u8003\u6848\u3002 \u30fb19\u4e16\u7d00\u534a\u3070\uff1a\u30c7\u30a3\u30ea\u30af\u30ec\u304c\u7d1a\u6570\u3068\u7a4d\u5206\u8868\u793a\u3092\u6574\u7406\u3002 \u30fb1859\u5e74\uff1a\u30ea\u30fc\u30de\u30f3\u304c\u8907\u7d20\u89e3\u6790\u7684\u624b\u6cd5\u3067 \u03b6(s) \u306e\u89e3\u6790\u63a5\u7d9a\u3068\u95a2\u6570\u65b9\u7a0b\u5f0f\u3092\u767a\u8868\u3002 \u30fb20\u4e16\u7d00\u4ee5\u964d\uff1a\u30ea\u30fc\u30de\u30f3\u4e88\u60f3\u306e\u5468\u8fba\u3067\u89e3\u6790\u7684\u6570\u8ad6\u304c\u5927\u767a\u5c55\u3057\u3001\u30d7\u30e9\u30a4\u30e0\u30ab\u30a6\u30f3\u30c8\u95a2\u6570 \u03c0(x) \u3068\u306e\u95a2\u4fc2\u304c\u6df1\u304f\u7814\u7a76\u3055\u308c\u305f\u3002<\/p>\n<p>\uff13\uff0e\u5b9a\u7fa9\u3068\u57fa\u672c\u6027\u8cea 1) \u7d1a\u6570\u8868\u793a\uff08Re(s)&gt;1\uff09 \u3000\u03b6(s) = \u03a3_{n=1}\u221e 1\/n^s 2) \u30aa\u30a4\u30e9\u30fc\u7a4d\u8868\u793a\uff08Re(s)&gt;1\uff09 \u3000\u03b6(s) = \u03a0_{p:\u7d20\u6570} (1 \u2212 p^{\u2212s})^{\u22121} 3) \u89e3\u6790\u63a5\u7d9a \u3000\u03b6(s) \u306f s = 1 \u3067\u5358\u6975\u3092\u3082\u3064\u304c\u3001\u4ed6\u306e\u5168\u70b9\u3067\u6b63\u5247\u95a2\u6570\u3068\u3057\u3066\u62e1\u5f35\u53ef\u80fd\u3002 4) \u95a2\u6570\u65b9\u7a0b\u5f0f \u3000\u03be(s) = \u03c0^{\u2212s\/2} \u0393(s\/2) \u03b6(s) \u306f s \u2192 1\u2212s \u306e\u5bfe\u79f0\u6027\u3092\u3082\u3064\u3002<\/p>\n<p>\uff14\uff0e\u5fdc\u7528\u4f8b\u30fb\u95a2\u9023\u5206\u91ce \u30fb\u7d20\u6570\u5b9a\u7406\uff1a\u03c0(x) \u223c x \/ log x \u306e\u8a3c\u660e\u306b \u03b6(s) \u306e\u96f6\u70b9\u5206\u5e03\u304c\u91cd\u8981\u3002 \u30fb\u30ea\u30fc\u30de\u30f3\u4e88\u60f3\uff1a\u975e\u81ea\u660e\u96f6\u70b9\u304c Re(s)=1\/2 \u306e\u76f4\u7dda\u4e0a\u306b\u5b58\u5728\u3059\u308b\u304b\u304c\u672a\u89e3\u6c7a\u3002 \u30fb\u91cf\u5b50\u529b\u5b66\u30fb\u7d71\u8a08\u529b\u5b66\uff1a\u30a8\u30cd\u30eb\u30ae\u30fc\u30b9\u30da\u30af\u30c8\u30eb\u306e\u7121\u9650\u7d1a\u6570\u306e\u6b63\u5247\u5316\u3002 \u30fb\u6697\u53f7\u7406\u8ad6\uff1a\u5927\u304d\u306a\u7d20\u56e0\u6570\u5206\u89e3\u306e\u8a08\u7b97\u8907\u96d1\u5ea6\u89e3\u6790\u3002 \u30fb\u78ba\u7387\u8ad6\u30fb\u30d5\u30e9\u30af\u30bf\u30eb\uff1a\u81ea\u5df1\u76f8\u4f3c\u69cb\u9020\u3084\u591a\u5909\u91cf\u30bc\u30fc\u30bf\u95a2\u6570\u3078\u306e\u62e1\u5f35\u7814\u7a76\u3002<\/p>\n<p>\uff15\uff0e\u7814\u7a76\u306e\u73fe\u72b6 \u30ea\u30fc\u30de\u30f3\u4e88\u60f3\u306f\u672a\u89e3\u6c7a\u3067\u3042\u308a\u3001\u30df\u30ec\u30cb\u30a2\u30e0\u61f8\u8cde\u554f\u984c\u306e\u4e00\u3064\u306b\u9078\u3070\u308c\u3066\u3044\u307e\u3059\u3002\u8a08\u7b97\u6a5f\u306b\u3088\u308b\u96f6\u70b9\u63a2\u7d22\u306f 10^13 \u500b\u4ee5\u4e0a\u306e\u975e\u81ea\u660e\u96f6\u70b9\u304c Re(s)=1\/2 \u4e0a\u306b\u3042\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3057\u3066\u3044\u307e\u3059\u304c\u3001\u4e00\u822c\u8a3c\u660e\u306f\u5f97\u3089\u308c\u3066\u3044\u307e\u305b\u3093\u3002\u4e00\u65b9\u3067\u3001\u30e2\u30c6\u30a3\u30d6\u30bc\u30fc\u30bf\u95a2\u6570\u3084\u591a\u5909\u6570\u30bc\u30fc\u30bf\u95a2\u6570\u3001p \u9032\u30bc\u30fc\u30bf\u95a2\u6570\u306a\u3069\u3001\u62e1\u5f35\u7248\u306e\u7814\u7a76\u3082\u6d3b\u767a\u3067\u3059\u3002<\/p>\n<p>\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u3008\u7279\u5fb4\uff085\u9805\u76ee\u4ee5\u4e0a\uff09\u3009 1. \u7d1a\u6570\u8868\u793a\u3068\u30aa\u30a4\u30e9\u30fc\u7a4d\u8868\u793a\u306e\u4e8c\u91cd\u69cb\u9020\u3092\u3082\u3064\u3002 2. \u30ea\u30fc\u30de\u30f3\u4e88\u60f3\u3068\u3044\u3046\u672a\u89e3\u6c7a\u554f\u984c\u3092\u4e2d\u5fc3\u306b\u6570\u8ad6\u754c\u30fb\u89e3\u6790\u5b66\u754c\u3067\u7814\u7a76\u304c\u9032\u3080\u3002 3. \u95a2\u6570\u65b9\u7a0b\u5f0f\u306b\u3088\u308a s \u2194 1\u2212s \u306e\u5bfe\u79f0\u6027\u3092\u5099\u3048\u308b\u3002 4. \u89e3\u6790\u63a5\u7d9a\u306b\u3088\u308a s=1 \u4ee5\u5916\u306e\u5168\u8907\u7d20\u5e73\u9762\u3067\u6b63\u5247\u306b\u62e1\u5f35\u53ef\u80fd\u3002 5. \u91cf\u5b50\u5834\u7406\u8ad6\u306a\u3069\u7269\u7406\u5b66\u3078\u306e\u5fdc\u7528\u3068\u3057\u3066 \u03b6-\u95a2\u6570\u6b63\u5247\u5316\u304c\u3042\u308b\u3002 6. \u975e\u81ea\u660e\u96f6\u70b9\u306e\u5206\u5e03\u304c\u7d20\u6570\u5206\u5e03\u3068\u6df1\u3044\u95a2\u4fc2\u3092\u3082\u3064\u3002 7. \u591a\u5909\u6570\u30fbp\u9032\u30fb\u52d5\u6a5f\u4ed8\u3051\u30bc\u30fc\u30bf\u95a2\u6570\u306a\u3069\u591a\u69d8\u306a\u62e1\u5f35\u304c\u3042\u308b\u3002<\/p>\n<p>\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u3008\u53c2\u8003\u6587\u732e\u30fb\u30b5\u30a4\u30c8\u3009 1. \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2\u300c\u30ea\u30fc\u30de\u30f3\u30bc\u30fc\u30bf\u95a2\u6570\u300d <a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E3%83%AA%E3%83%BC%E3%83%9E%E3%83%B3%E3%82%BC%E3%83%BC%E3%82%BF%E5%87%BD%E6%95%B0\">https:\/\/ja.wikipedia.org\/wiki\/\u30ea\u30fc\u30de\u30f3\u30bc\u30fc\u30bf\u51fd\u6570<\/a> 2. \u6570\u5b66\u8f9e\u5178\uff08\u5ca9\u6ce2\u6570\u5b66\u8f9e\u5178\uff09\u300c\u30bc\u30fc\u30bf\u95a2\u6570\u300d <a href=\"https:\/\/kotobank.jp\/word\/%E3%82%BC%E3%83%BC%E3%82%BF%E9%96%A2%E6%95%B0-183763\">https:\/\/kotobank.jp\/word\/\u30bc\u30fc\u30bf\u95a2\u6570-183763<\/a> 3. \u6771\u4eac\u5927\u5b66\u6570\u7406\u79d1\u5b66\u7814\u7a76\u79d1\u300c\u30ea\u30fc\u30de\u30f3\u30bc\u30fc\u30bf\u95a2\u6570\u3068\u30ea\u30fc\u30de\u30f3\u4e88\u60f3\u300d <a href=\"https:\/\/www.ms.u-tokyo.ac.jp\/~tour\/research\/zeta.html\">https:\/\/www.ms.u-tokyo.ac.jp\/~tour\/research\/zeta.html<\/a> 4. Clay Mathematics Institute\u300cMillennium Prize Problems \u2013 Riemann Hypothesis\u300d <a href=\"https:\/\/www.claymath.org\/millennium-problems\/riemann-hypothesis\">https:\/\/www.claymath.org\/millennium-problems\/riemann-hypothesis<\/a> 5. \u65e5\u672c\u7269\u7406\u5b66\u4f1a\u8a8c\u300c\u30bc\u30fc\u30bf\u95a2\u6570\u6b63\u5247\u5316\u3068\u7269\u7406\u5b66\u3078\u306e\u5fdc\u7528\u300d <a href=\"https:\/\/www.jps.or.jp\/books\/journal\/77-4\/77-4-797.pdf\">https:\/\/www.jps.or.jp\/books\/journal\/77-4\/77-4-797.pdf<\/a> (PDF) 6. arXiv\u300cAn introduction to the Riemann zeta-function\u300d (\u82f1\u8a9e) <a href=\"https:\/\/arxiv.org\/abs\/math\/0402358\">https:\/\/arxiv.org\/abs\/math\/0402358<\/a><\/p>\n<p>\u4ee5\u4e0a\u304c\u30ea\u30fc\u30de\u30f3\u30bc\u30fc\u30bf\u95a2\u6570\u306e\u6982\u8aac\u3001\u7279\u5fb4\u3001\u304a\u3088\u3073\u53c2\u8003\u60c5\u5831\u3067\u3059\u3002<\/p>\n<p><a href=\"https:\/\/wordpress.realcollector.jp\/blog\/wp-content\/uploads\/2025\/12\/current_stablediffusion_api_response-216.png\" rel=\"attachment wp-att-65509\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"65509\" data-permalink=\"https:\/\/wordpress.realcollector.jp\/blog\/?attachment_id=65509\" data-orig-file=\"https:\/\/wordpress.realcollector.jp\/blog\/wp-content\/uploads\/2025\/12\/current_stablediffusion_api_response-216.png\" data-orig-size=\"512,512\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"current_stablediffusion_api_response\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/wordpress.realcollector.jp\/blog\/wp-content\/uploads\/2025\/12\/current_stablediffusion_api_response-216-300x300.png\" data-large-file=\"https:\/\/wordpress.realcollector.jp\/blog\/wp-content\/uploads\/2025\/12\/current_stablediffusion_api_response-216.png\" src=\"https:\/\/wordpress.realcollector.jp\/blog\/wp-content\/uploads\/2025\/12\/current_stablediffusion_api_response-216.png\" alt=\"\" title=\"current_stablediffusion_api_response-216-png\" width=\"1024\" height=\"1024\" class=\"alignnone size-full wp-image-65509\" srcset=\"https:\/\/wordpress.realcollector.jp\/blog\/wp-content\/uploads\/2025\/12\/current_stablediffusion_api_response-216.png 512w, https:\/\/wordpress.realcollector.jp\/blog\/wp-content\/uploads\/2025\/12\/current_stablediffusion_api_response-216-300x300.png 300w, 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