English

Algebraic identities among $q$- analogue of Euler double zeta values

Number Theory 2024-04-12 v1

Abstract

In 2003, Zudilin presented a qq-analogue of Euler's identity for one of the variants of qq-double zeta function. This article focuses on exploring identities related to another variant of qq-double zeta function and its star variant. Using a qq-analogue of the Nielsen Reflexion Formula for q>1q>1, we investigate identities involving different versions of qq-analogues of the Riemann zeta function and the double-zeta function. Additionally, we analyze the behavior of ζq(s1,s2)\zeta_q(s_1, s_2) as s1s_1 and s2s_2 approach to 00 and compare these limits to those of the classical double-zeta function. Finally, we discuss the qq-analogue of the Mordell-Tornheim rr-ple zeta function and its relation with the qq-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}
}