Algebraic identities among $q$- analogue of Euler double zeta values
Number Theory
2024-04-12 v1
Abstract
In 2003, Zudilin presented a -analogue of Euler's identity for one of the variants of -double zeta function. This article focuses on exploring identities related to another variant of -double zeta function and its star variant. Using a -analogue of the Nielsen Reflexion Formula for , we investigate identities involving different versions of -analogues of the Riemann zeta function and the double-zeta function. Additionally, we analyze the behavior of as and approach to and compare these limits to those of the classical double-zeta function. Finally, we discuss the -analogue of the Mordell-Tornheim -ple zeta function and its relation with the -double zeta function.
Keywords
Cite
@article{arxiv.2404.07688,
title = {Algebraic identities among $q$- analogue of Euler double zeta values},
author = {Tapas Chatterjee and Sonam Garg},
journal= {arXiv preprint arXiv:2404.07688},
year = {2024}
}