{"id":552,"date":"2025-11-12T04:24:48","date_gmt":"2025-11-11T20:24:48","guid":{"rendered":"http:\/\/lixinliu-jlu.top\/?p=552"},"modified":"2026-02-18T12:33:08","modified_gmt":"2026-02-18T04:33:08","slug":"%e7%94%b0%e9%87%8e%e9%99%a2%e5%a3%ab%e5%9b%a2%e9%98%9f%e6%88%90%e6%9e%9c%e8%8e%b7%e6%95%b0%e5%ad%a6%e9%a1%b6%e5%88%8a%e6%8e%a5%e5%8f%97%ef%bc%8c%e7%a0%b4%e8%a7%a3%e6%95%b0%e8%ae%ba%e9%a2%86%e5%9f%9f","status":"publish","type":"post","link":"https:\/\/zeroner.cn\/index.php\/2025\/11\/12\/%e7%94%b0%e9%87%8e%e9%99%a2%e5%a3%ab%e5%9b%a2%e9%98%9f%e6%88%90%e6%9e%9c%e8%8e%b7%e6%95%b0%e5%ad%a6%e9%a1%b6%e5%88%8a%e6%8e%a5%e5%8f%97%ef%bc%8c%e7%a0%b4%e8%a7%a3%e6%95%b0%e8%ae%ba%e9%a2%86%e5%9f%9f\/","title":{"rendered":"\u7530\u91ce\u9662\u58eb\u56e2\u961f\u6210\u679c\u83b7\u6570\u5b66\u9876\u520a\u63a5\u53d7\uff0c\u7834\u89e3\u6570\u8bba\u9886\u57df\u91cd\u8981\u96be\u9898"},"content":{"rendered":"\n<p>\u91d1\u79cb\u5341\u6708\uff0c\u7855\u679c\u76c8\u679d\u30022025\u5e7410\u6708\uff0c\u4e2d\u56fd\u6570\u5b66\u9886\u57df\u4f20\u6765\u91cd\u78c5\u559c\u8baf\uff0c\u4e2d\u56fd\u79d1\u5b66\u9662\u6570\u5b66\u4e0e\u7cfb\u7edf\u79d1\u5b66\u7814\u7a76\u9662\u7530\u91ce\u9662\u58eb\u4e0e\u7f8e\u56fd\u52a0\u5dde\u7406\u5de5\u5b66\u9662\u5b66\u8005Ashay A. Burungale\u5408\u4f5c\u7684\u7814\u7a76\u6210\u679c\uff0c\u6b63\u5f0f\u88ab\u6570\u5b66\u56db\u5927\u9876\u7ea7\u671f\u520a\u4e4b\u4e00\u7684\u300aAnnals of Mathematics\u300b\uff08\u300a\u6570\u5b66\u5e74\u520a\u300b\uff09\u63a5\u6536\uff0c\u8be5\u6210\u679c\u6210\u529f\u7834\u89e3\u4e86\u6570\u8bba\u9886\u57df\u7684\u5173\u952e\u96be\u9898\uff0c\u586b\u8865\u4e86\u76f8\u5173\u7814\u7a76\u7a7a\u767d\uff0c\u4e3a\u56fd\u9645\u6570\u8bba\u7814\u7a76\u6ce8\u5165\u4e2d\u56fd\u529b\u91cf\uff0c\u6210\u4e3a\u5f53\u6708\u6570\u5b66\u9886\u57df\u6700\u5177\u5f71\u54cd\u529b\u7684\u91cd\u5927\u4e8b\u4ef6\u3002<\/p>\n\n\n\n<p>\u636e\u4e2d\u56fd\u79d1\u5b66\u9662\u6570\u5b66\u4e0e\u7cfb\u7edf\u79d1\u5b66\u7814\u7a76\u966210\u670814\u65e5\u5b98\u65b9\u53d1\u5e03\uff0c\u6b64\u6b21\u88ab\u9876\u520a\u63a5\u6536\u7684\u6587\u7ae0\u9898\u4e3a\u300aA rank zero p-converse to a theorem of Gross\u2013Zagier, Kolyvagin and Rubin\uff08\u5bf9Gross\u2013Zagier\u3001Kolyvagin\u548cRubin\u5b9a\u7406\u7684\u4e00\u4e2a\u96f6\u79e9p-\u9006\u5b9a\u7406\uff09\u300b\uff0c\u76f8\u5173\u6210\u679c\u4e8e10\u670810\u65e5\u5728\u8be5\u671f\u520a\u201c\u5373\u5c06\u53d1\u8868\u6587\u7ae0\u201d\u680f\u76ee\u6b63\u5f0f\u516c\u5e03\uff0c\u6807\u5fd7\u7740\u6211\u56fd\u5728\u692d\u5706\u66f2\u7ebf\u4e0e\u6570\u8bba\u4ea4\u53c9\u9886\u57df\u7684\u7814\u7a76\u8fbe\u5230\u56fd\u9645\u9886\u5148\u6c34\u5e73\u3002<\/p>\n\n\n\n<p>\u636e\u6089\uff0c\u8be5\u7814\u7a76\u805a\u7126\u6709\u7406\u6570\u57df\u4e0a\u7684CM\u692d\u5706\u66f2\u7ebf\u8fd9\u4e00\u6838\u5fc3\u7814\u7a76\u5bf9\u8c61\uff0c\u56f4\u7ed5p\u221e-Selmer\u7fa4\u4e0e\u590dL-\u51fd\u6570\u7684\u5173\u8054\u5c55\u5f00\u6df1\u5165\u63a2\u7d22\uff0c\u6700\u7ec8\u53d6\u5f97\u7a81\u7834\u6027\u7ed3\u8bba\uff1a\u8bbeE\u662f\u5b9a\u4e49\u5728\u6709\u7406\u6570\u57df\u211a\u4e0a\u7684CM\u692d\u5706\u66f2\u7ebf\uff0cp\u4e3a\u4efb\u610f\u7d20\u6570\uff0c\u82e5\u2124\u209a-\u79e9corank_\u2124\u209a Sel\u209a\u221e(E\/\u211a)=0\uff0c\u5219\u5fc5\u6709\u5173\u8054L-\u51fd\u6570\u5728s=1\u5904\u7684\u9636ord\u209b=\u2081 L(s,E\/\u211a)=0\u3002\u8fd9\u4e00\u7ed3\u8bba\u7684\u8bde\u751f\uff0c\u4e0d\u4ec5\u5b8c\u5584\u4e86Gross\u2013Zagier\u3001Kolyvagin\u548cRubin\u5b9a\u7406\u7684\u7406\u8bba\u4f53\u7cfb\uff0c\u66f4\u5b9e\u73b0\u4e86\u5076parity \u201cGoldfeld\u731c\u60f3\u201d\u9996\u4e2a\u5b9e\u4f8b\u7684\u7a81\u7834\u2014\u2014\u5728\u6240\u6709\u6b63\u65e0\u5e73\u65b9\u56e0\u5b50\u6574\u6570n\u4e2d\uff0c\u670950%\u6ee1\u8db3\u201cE(n)\u7684L-\u51fd\u6570\u5728s=1\u5904\u7684\u9636ord\u209b=\u2081 L(s,E(n)\/\u211a)=0\u201d\uff0c\u5176\u4e2dE(n):ny\u00b2=x\u00b3\u2212x\u662f\u540c\u4f59\u6570\u692d\u5706\u66f2\u7ebfE:y\u00b2=x\u00b3\u2212x\u7684\u4e8c\u6b21\u626d\u8f6c\u3002<\/p>\n\n\n\n<p>\u503c\u5f97\u5173\u6ce8\u7684\u662f\uff0c\u8fd9\u9879\u5177\u6709\u91cc\u7a0b\u7891\u610f\u4e49\u7684\u6210\u679c\uff0c\u5386\u7ecf\u8fd16\u5e74\u7684\u4e25\u683c\u5ba1\u7a3f\u6253\u78e8\uff0c\u51dd\u805a\u4e86\u4e24\u4f4d\u7814\u7a76\u8005\u7684\u957f\u671f\u5fc3\u8840\u3002\u65e9\u57282020\u5e74\uff0c\u7530\u91ce\u9662\u58eb\u4e0eAshay A. Burungale\u5c31\u66fe\u5728\u8be5\u9886\u57df\u53d6\u5f97\u91cd\u8981\u8fdb\u5c55\uff0c\u5176\u5408\u4f5c\u6210\u679c\u5df2\u53d1\u8868\u4e8e\u53e6\u4e00\u672c\u6570\u5b66\u56db\u5927\u9876\u520a\u300aInventiones Mathematicae\u300b\uff08\u300a\u6570\u5b66\u65b0\u8fdb\u5c55\u300b\uff09\uff0c\u6b64\u6b21\u63a5\u6536\u7684\u6210\u679c\u662f\u4e24\u4eba\u5728\u8be5\u9886\u57df\u7684\u518d\u5ea6\u6df1\u5ea6\u5408\u4f5c\u4e0e\u91cd\u5927\u7a81\u7834\uff0c\u5f70\u663e\u4e86\u79d1\u7814\u5de5\u4f5c\u8005\u6f5c\u5fc3\u94bb\u7814\u3001\u4e45\u4e45\u4e3a\u529f\u7684\u575a\u5b88\u3002<\/p>\n\n\n\n<p>\u7530\u91ce\u9662\u58eb\u957f\u671f\u6df1\u8015\u6570\u8bba\u9886\u57df\uff0c\u5728\u692d\u5706\u66f2\u7ebf\u3001\u81ea\u5b88\u5f62\u5f0f\u7b49\u76f8\u5173\u7814\u7a76\u4e2d\u6210\u679c\u4e30\u7855\uff0c\u6b64\u6b21\u5408\u4f5c\u6210\u679c\u7684\u53d1\u8868\uff0c\u4e0d\u4ec5\u8fdb\u4e00\u6b65\u5de9\u56fa\u4e86\u6211\u56fd\u5728\u6570\u8bba\u9886\u57df\u7684\u56fd\u9645\u5f71\u54cd\u529b\uff0c\u66f4\u4e3a\u5168\u7403\u76f8\u5173\u9886\u57df\u7684\u7814\u7a76\u63d0\u4f9b\u4e86\u5168\u65b0\u7684\u601d\u8def\u548c\u65b9\u6cd5\uff0c\u5bf9\u63a8\u52a8\u692d\u5706\u66f2\u7ebf\u7406\u8bba\u3001\u6570\u8bba\u53ca\u4ee3\u6570\u51e0\u4f55\u7b49\u4ea4\u53c9\u5b66\u79d1\u7684\u53d1\u5c55\u5177\u6709\u91cd\u8981\u7684\u5b66\u672f\u4ef7\u503c\u548c\u6307\u5bfc\u610f\u4e49\u3002<\/p>\n\n\n\n<p>\u4e1a\u5185\u4e13\u5bb6\u8bc4\u4ef7\uff0c\u8be5\u6210\u679c\u9996\u6b21\u7ed9\u51fa\u5076parity \u201cGoldfeld\u731c\u60f3\u201d\u7684\u5b9e\u4f8b\uff0c\u89e3\u51b3\u4e86\u56f0\u6270\u5b66\u754c\u591a\u5e74\u7684\u5173\u952e\u7406\u8bba\u96be\u9898\uff0c\u5176\u4e25\u8c28\u7684\u8bba\u8bc1\u8fc7\u7a0b\u548c\u521b\u65b0\u6027\u7684\u7814\u7a76\u601d\u8def\uff0c\u4e3a\u540e\u7eed\u76f8\u5173\u7814\u7a76\u5960\u5b9a\u4e86\u575a\u5b9e\u57fa\u7840\u3002\u968f\u7740\u8fd9\u9879\u6210\u679c\u7684\u6b63\u5f0f\u53d1\u8868\uff0c\u5c06\u5438\u5f15\u66f4\u591a\u5168\u7403\u5b66\u8005\u6295\u8eab\u8be5\u9886\u57df\u7684\u63a2\u7d22\uff0c\u52a9\u529b\u6570\u8bba\u7814\u7a76\u8fc8\u5411\u65b0\u7684\u9ad8\u5ea6\uff0c\u4e5f\u8ba9\u4e16\u754c\u770b\u5230\u4e2d\u56fd\u6570\u5b66\u57fa\u7840\u7814\u7a76\u7684\u5f3a\u52b2\u53d1\u5c55\u52bf\u5934\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u91d1\u79cb\u5341\u6708\uff0c\u7855\u679c\u76c8\u679d\u30022025\u5e7410\u6708\uff0c\u4e2d\u56fd\u6570\u5b66\u9886\u57df\u4f20\u6765\u91cd\u78c5\u559c\u8baf\uff0c\u4e2d\u56fd\u79d1\u5b66\u9662\u6570\u5b66\u4e0e\u7cfb\u7edf\u79d1\u5b66\u7814\u7a76\u9662\u7530\u91ce\u9662\u58eb\u4e0e\u7f8e\u56fd\u52a0\u5dde\u7406\u5de5\u5b66\u9662\u5b66\u8005Ashay A. Burungale\u5408\u4f5c\u7684\u7814\u7a76\u6210\u679c\uff0c\u6b63\u5f0f\u88ab\u6570\u5b66\u56db\u5927\u9876\u7ea7\u671f\u520a\u4e4b<\/p>\n<p><a href=\"https:\/\/zeroner.cn\/index.php\/2025\/11\/12\/%e7%94%b0%e9%87%8e%e9%99%a2%e5%a3%ab%e5%9b%a2%e9%98%9f%e6%88%90%e6%9e%9c%e8%8e%b7%e6%95%b0%e5%ad%a6%e9%a1%b6%e5%88%8a%e6%8e%a5%e5%8f%97%ef%bc%8c%e7%a0%b4%e8%a7%a3%e6%95%b0%e8%ae%ba%e9%a2%86%e5%9f%9f\/\" class=\"av-btn av-btn-secondary av-btn-bubble\">\u4e86\u89e3\u66f4\u591a<span class=\"screen-reader-text\">\u7530\u91ce\u9662\u58eb\u56e2\u961f\u6210\u679c\u83b7\u6570\u5b66\u9876\u520a\u63a5\u53d7\uff0c\u7834\u89e3\u6570\u8bba\u9886\u57df\u91cd\u8981\u96be\u9898<\/span><i class=\"fa fa-arrow-right\"><\/i><span class=\"bubble_effect\"><span class=\"circle top-left\"><\/span><span class=\"circle top-left\"><\/span><span class=\"circle top-left\"><\/span><span class=\"button effect-button\"><\/span><span class=\"circle bottom-right\"><\/span><span class=\"circle bottom-right\"><\/span><span class=\"circle bottom-right\"><\/span><\/span><\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-552","post","type-post","status-publish","format-standard","hentry","category-3"],"_links":{"self":[{"href":"https:\/\/zeroner.cn\/index.php\/wp-json\/wp\/v2\/posts\/552","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/zeroner.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/zeroner.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/zeroner.cn\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/zeroner.cn\/index.php\/wp-json\/wp\/v2\/comments?post=552"}],"version-history":[{"count":1,"href":"https:\/\/zeroner.cn\/index.php\/wp-json\/wp\/v2\/posts\/552\/revisions"}],"predecessor-version":[{"id":553,"href":"https:\/\/zeroner.cn\/index.php\/wp-json\/wp\/v2\/posts\/552\/revisions\/553"}],"wp:attachment":[{"href":"https:\/\/zeroner.cn\/index.php\/wp-json\/wp\/v2\/media?parent=552"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zeroner.cn\/index.php\/wp-json\/wp\/v2\/categories?post=552"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zeroner.cn\/index.php\/wp-json\/wp\/v2\/tags?post=552"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}