对称方形l函数周期的线性无关性

IF 0.4 Q3 MATHEMATICS

Annales Mathematiques du Quebec Pub Date : 2025-09-13 DOI:10.1007/s40316-025-00258-7

Tianyu Ni, Hui Xue

{"title":"对称方形l函数周期的线性无关性","authors":"Tianyu Ni, Hui Xue","doi":"10.1007/s40316-025-00258-7","DOIUrl":null,"url":null,"abstract":"<div>For \\(S_k\\), the space of cusp forms of weight k for the full modular group, we first introduce periods on \\(S_k\\) associated to symmetric square L-functions. We then prove that for a fixed natural number n, if k is sufficiently large relative to n, then any n such periods are linearly independent. With some extra assumption, we also prove that for \\(k\\ge e^{12}\\), we can always pick up to \\(\\frac{\\log k}{4}\\) arbitrary linearly independent periods.</div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 2","pages":"445 - 462"},"PeriodicalIF":0.4000,"publicationDate":"2025-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Linear independence of periods for the symmetric square L-functions\",\"authors\":\"Tianyu Ni, Hui Xue\",\"doi\":\"10.1007/s40316-025-00258-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>For \\\\(S_k\\\\), the space of cusp forms of weight k for the full modular group, we first introduce periods on \\\\(S_k\\\\) associated to symmetric square L-functions. We then prove that for a fixed natural number n, if k is sufficiently large relative to n, then any n such periods are linearly independent. With some extra assumption, we also prove that for \\\\(k\\\\ge e^{12}\\\\), we can always pick up to \\\\(\\\\frac{\\\\log k}{4}\\\\) arbitrary linearly independent periods.</div>\",\"PeriodicalId\":42753,\"journal\":{\"name\":\"Annales Mathematiques du Quebec\",\"volume\":\"49 2\",\"pages\":\"445 - 462\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2025-09-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Mathematiques du Quebec\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40316-025-00258-7\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Mathematiques du Quebec","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40316-025-00258-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

对于满模群的权k的尖点形式空间\(S_k\)，我们首先在\(S_k\)上引入与对称方形l函数相关的周期。然后证明对于一个固定的自然数n，如果k相对于n足够大，那么任意n个这样的周期都是线性无关的。通过一些额外的假设，我们也证明了对于\(k\ge e^{12}\)，我们总是可以取到\(\frac{\log k}{4}\)任意线性无关的周期。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Linear independence of periods for the symmetric square L-functions

For \(S_k\), the space of cusp forms of weight k for the full modular group, we first introduce periods on \(S_k\) associated to symmetric square L-functions. We then prove that for a fixed natural number n, if k is sufficiently large relative to n, then any n such periods are linearly independent. With some extra assumption, we also prove that for \(k\ge e^{12}\), we can always pick up to \(\frac{\log k}{4}\) arbitrary linearly independent periods.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Annales Mathematiques du Quebec MATHEMATICS-

CiteScore

1.10

自引率

0.00%

发文量

期刊介绍： The goal of the Annales mathématiques du Québec (formerly: Annales des sciences mathématiques du Québec) is to be a high level journal publishing articles in all areas of pure mathematics, and sometimes in related fields such as applied mathematics, mathematical physics and computer science. Papers written in French or English may be submitted to one of the editors, and each published paper will appear with a short abstract in both languages. History: The journal was founded in 1977 as „Annales des sciences mathématiques du Québec”, in 2013 it became a Springer journal under the name of “Annales mathématiques du Québec”. From 1977 to 2018, the editors-in-chief have respectively been S. Dubuc, R. Cléroux, G. Labelle, I. Assem, C. Levesque, D. Jakobson, O. Cornea. Les Annales mathématiques du Québec (anciennement, les Annales des sciences mathématiques du Québec) se veulent un journal de haut calibre publiant des travaux dans toutes les sphères des mathématiques pures, et parfois dans des domaines connexes tels les mathématiques appliquées, la physique mathématique et l''informatique. On peut soumettre ses articles en français ou en anglais à l''éditeur de son choix, et les articles acceptés seront publiés avec un résumé court dans les deux langues. Histoire: La revue québécoise “Annales des sciences mathématiques du Québec” était fondée en 1977 et est devenue en 2013 une revue de Springer sous le nom Annales mathématiques du Québec. De 1977 à 2018, les éditeurs en chef ont respectivement été S. Dubuc, R. Cléroux, G. Labelle, I. Assem, C. Levesque, D. Jakobson, O. Cornea.