修正双zeta值的模形式和q-类似物

IF 0.4 4区数学 Q4 MATHEMATICS

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2020-11-11 DOI:10.1007/s12188-020-00227-7

Henrik Bachmann

{"title":"修正双zeta值的模形式和q-类似物","authors":"Henrik Bachmann","doi":"10.1007/s12188-020-00227-7","DOIUrl":null,"url":null,"abstract":"<div><p>We present explicit formulas for Hecke eigenforms as linear combinations of q-analogues of modified double zeta values. As an application, we obtain period polynomial relations and sum formulas for these modified double zeta values. These relations have similar shapes as the period polynomial relations of Gangl, Kaneko, and Zagier and the usual sum formulas for classical double zeta values.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2020-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-020-00227-7","citationCount":"3","resultStr":"{\"title\":\"Modular forms and q-analogues of modified double zeta values\",\"authors\":\"Henrik Bachmann\",\"doi\":\"10.1007/s12188-020-00227-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We present explicit formulas for Hecke eigenforms as linear combinations of q-analogues of modified double zeta values. As an application, we obtain period polynomial relations and sum formulas for these modified double zeta values. These relations have similar shapes as the period polynomial relations of Gangl, Kaneko, and Zagier and the usual sum formulas for classical double zeta values.</p></div>\",\"PeriodicalId\":50932,\"journal\":{\"name\":\"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2020-11-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s12188-020-00227-7\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s12188-020-00227-7\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s12188-020-00227-7","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 3

摘要

我们给出了作为修正双zeta值的q-类似物的线性组合的Hecke特征型的显式公式。作为应用，我们得到了这些修正后的双zeta值的周期多项式关系和求和公式。这些关系与Gangl, Kaneko和Zagier的周期多项式关系以及经典双zeta值的通常和公式具有相似的形状。

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

Modular forms and q-analogues of modified double zeta values

We present explicit formulas for Hecke eigenforms as linear combinations of q-analogues of modified double zeta values. As an application, we obtain period polynomial relations and sum formulas for these modified double zeta values. These relations have similar shapes as the period polynomial relations of Gangl, Kaneko, and Zagier and the usual sum formulas for classical double zeta values.

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

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.