Algebraic identities among q- analogue of Euler double zeta values

2024/04/11 by Tapas Chatterjee, Chatterjee, Tapas, Sonam Garg +1
Mathematics · #Advanced Mathematical Identities #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2404.07688

openalex publication_date 2024/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 2003, Zudilin presented a q-analogue of Euler's identity for one of the variants of q-double zeta function. This article focuses on exploring identities related to another variant of q-double zeta function and its star variant. Using a q-analogue of the Nielsen Reflexion Formula for q>1, we investigate identities involving different versions of q-analogues of the Riemann zeta function and the double-zeta function. Additionally, we analyze the behavior of ζ_q(s₁, s₂) as s₁ and s₂ approach to 0 and compare these limits to those of the classical double-zeta function. Finally, we discuss the q-analogue of the Mordell-Tornheim r-ple zeta function and its relation with the q-double zeta function.

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