Mixed motives and linear forms in the Catalan constant

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Eskandari, Payman, Murty, Kumar, Nemoto, Yusuke
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866918307156721664
author Eskandari, Payman
Murty, Kumar
Nemoto, Yusuke
author_facet Eskandari, Payman
Murty, Kumar
Nemoto, Yusuke
contents We first give a geometric construction of a 2-dimensional mixed motive over $\mathbb{Q}$ with the Catalan constant $\mathbf{G}=1-1/3^2+1/5^2-1/7^2+\cdots$ as a period. We then use this motive to obtain a supply of linear forms in 1 and $\mathbf{G}$. We also explicitly compute the coefficients of 1 and $\mathbf{G}$ in these linear forms.
format Preprint
id arxiv_https___arxiv_org_abs_2510_20648
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Mixed motives and linear forms in the Catalan constant
Eskandari, Payman
Murty, Kumar
Nemoto, Yusuke
Number Theory
Algebraic Geometry
11G99, 11M06, 14F42
We first give a geometric construction of a 2-dimensional mixed motive over $\mathbb{Q}$ with the Catalan constant $\mathbf{G}=1-1/3^2+1/5^2-1/7^2+\cdots$ as a period. We then use this motive to obtain a supply of linear forms in 1 and $\mathbf{G}$. We also explicitly compute the coefficients of 1 and $\mathbf{G}$ in these linear forms.
title Mixed motives and linear forms in the Catalan constant
topic Number Theory
Algebraic Geometry
11G99, 11M06, 14F42
url https://arxiv.org/abs/2510.20648