Journal of the Ramanujan Mathematical Society
Volume 40, Issue 2, June 2025 pp. 95–106.
Algebraic identities among q-analogue of Euler double zeta values
Authors:
Tapas Chatterjee and Sonam Garg
Author institution:Department of Mathematics, Indian Institute of Technology Ropar, Punjab, India.
Summary:
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}(s{1}, s{2}) as s{1} and s{2} 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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