{"title":"椭圆 L 函数 Dirichlet 扭曲的非零中心值","authors":"Hershy Kisilevsky, Jungbae Nam","doi":"10.1016/j.jnt.2024.07.003","DOIUrl":null,"url":null,"abstract":"<div><p>We consider heuristic predictions for small non-zero algebraic central values of twists of the <em>L</em>-function of an elliptic curve <span><math><mi>E</mi><mo>/</mo><mi>Q</mi></math></span> by Dirichlet characters. We provide computational evidence for these predictions and consequences of them for instances of an analogue of the Brauer-Siegel theorem associated to <span><math><mi>E</mi><mo>/</mo><mi>Q</mi></math></span> extended to chosen families of cyclic extensions of fixed degree.</p></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"266 ","pages":"Pages 166-194"},"PeriodicalIF":0.6000,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022314X24001719/pdfft?md5=a0edf993c65449e6ef9e685a75b7c9ac&pid=1-s2.0-S0022314X24001719-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Non-zero central values of Dirichlet twists of elliptic L-functions\",\"authors\":\"Hershy Kisilevsky, Jungbae Nam\",\"doi\":\"10.1016/j.jnt.2024.07.003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We consider heuristic predictions for small non-zero algebraic central values of twists of the <em>L</em>-function of an elliptic curve <span><math><mi>E</mi><mo>/</mo><mi>Q</mi></math></span> by Dirichlet characters. We provide computational evidence for these predictions and consequences of them for instances of an analogue of the Brauer-Siegel theorem associated to <span><math><mi>E</mi><mo>/</mo><mi>Q</mi></math></span> extended to chosen families of cyclic extensions of fixed degree.</p></div>\",\"PeriodicalId\":50110,\"journal\":{\"name\":\"Journal of Number Theory\",\"volume\":\"266 \",\"pages\":\"Pages 166-194\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-08-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0022314X24001719/pdfft?md5=a0edf993c65449e6ef9e685a75b7c9ac&pid=1-s2.0-S0022314X24001719-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Number Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022314X24001719\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Number Theory","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022314X24001719","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们考虑了关于椭圆曲线 E/Q 的 L 函数捻的非零代数中心值的启发式预测。我们提供了这些预测的计算证据，以及这些预测对与 E/Q 相关的布劳尔-西格尔定理的实例的影响，该定理扩展到固定度数的循环扩展的选定族。
Non-zero central values of Dirichlet twists of elliptic L-functions
We consider heuristic predictions for small non-zero algebraic central values of twists of the L-function of an elliptic curve by Dirichlet characters. We provide computational evidence for these predictions and consequences of them for instances of an analogue of the Brauer-Siegel theorem associated to extended to chosen families of cyclic extensions of fixed degree.
期刊介绍：
The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field.
The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory.
Starting in May 2019, JNT will have a new format with 3 sections:
JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access.
JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions.
Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
