Mixed motives and linear forms in the Catalan constant

IF 1.4 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2026-09-25 DOI:10.1112/jlms.70708

Payman Eskandari, V. Kumar Murty, Yusuke Nemoto

{"title":"Mixed motives and linear forms in the Catalan constant","authors":"Payman Eskandari, V. Kumar Murty, Yusuke Nemoto","doi":"10.1112/jlms.70708","DOIUrl":null,"url":null,"abstract":"We first give a geometric construction of a two-dimensional mixed motive over <math>\n <semantics>\n <mi>Q</mi>\n <annotation>${\\mathbb {Q}}$</annotation>\n </semantics></math> with the Catalan constant <math>\n <semantics>\n <mrow>\n <mi>G</mi>\n <mo>=</mo>\n <mn>1</mn>\n <mo>−</mo>\n <mn>1</mn>\n <mo>/</mo>\n <msup>\n <mn>3</mn>\n <mn>2</mn>\n </msup>\n <mo>+</mo>\n <mn>1</mn>\n <mo>/</mo>\n <msup>\n <mn>5</mn>\n <mn>2</mn>\n </msup>\n <mo>−</mo>\n <mn>1</mn>\n <mo>/</mo>\n <msup>\n <mn>7</mn>\n <mn>2</mn>\n </msup>\n <mo>+</mo>\n <mi>⋯</mi>\n </mrow>\n <annotation>${\\mathbf {G}}=1-1/3^2+1/5^2-1/7^2+\\cdots$</annotation>\n </semantics></math> as a period. We then use this motive to obtain a supply of linear forms in 1 and <math>\n <semantics>\n <mi>G</mi>\n <annotation>${\\mathbf {G}}$</annotation>\n </semantics></math>. We also explicitly compute the coefficients of 1 and <math>\n <semantics>\n <mi>G</mi>\n <annotation>${\\mathbf {G}}$</annotation>\n </semantics></math> in these linear forms.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 4","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70708","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/jlms.70708","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

Abstract

We first give a geometric construction of a two-dimensional mixed motive over $Q$ with the Catalan constant $G = 1 - 1 / 3^{2} + 1 / 5^{2} - 1 / 7^{2} + \dots$ as a period. We then use this motive to obtain a supply of linear forms in 1 and $G$ . We also explicitly compute the coefficients of 1 and $G$ in these linear forms.

查看原文本刊更多论文

加泰罗尼亚常数中的混合动机和线性形式

首先给出了Q ${\mathbb {Q}}$上具有加泰罗尼亚常数G = 1−1 / 32 + 1的二维混合动机的几何构造/5 2−1/7 2+⋯${\mathbf {G}}=1-1/3^2+1/5^2-1/7^2+\cdots$作为周期。然后，我们使用这个动机来获得1和G ${\mathbf {G}}$中的线性形式的供应。我们还显式地以这些线性形式计算1和G ${\mathbf {G}}$的系数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.