A \(q\)-analogue for Euler's evaluations of the Riemann zeta function

DOI10.1007/s40993-018-0141-yzbMath1459.11050arXiv1803.02467OpenAlexW2889990737WikidataQ128995690 ScholiaQ128995690MaRDI QIDQ2316316

Ankush Goswami

Publication date: 26 July 2019

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.02467

zbMATH Keywords

Riemann zeta functionStirling numbers of second kindupper half planetriangular numbers

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Binomial coefficients; factorials; (q)-identities (11B65) (zeta (s)) and (L(s, chi)) (11M06)

Related Items (4)

\(q\)-analogues of some series for powers of \(\pi\) ⋮ On two double series for \(\pi\) and their \(q\)-analogues ⋮ A \(q\)-analogue for Euler's \(\zeta(6) = \pi^6/945\) ⋮ Green’s Functions and Euler’s Formula for $$\zeta (2n)$$

Cites Work

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• An asymptotic for the representation of integers as sums of triangular numbers
• Partition-theoretic formulas for arithmetic densities
• Diophantine problems for \(q\)-zeta values
• On the representation of integers as sums of triangular numbers
• A \(q\)-analogue for Euler's \(\zeta(6) = \pi^6/945\)
• SÉRIES HYPERGÉOMÉTRIQUES BASIQUES, $q$-ANALOGUES DES VALEURS DE LA FONCTION ZÊTA ET SÉRIES D’EISENSTEIN
• Two $q$-analogues of Euler’s formula $\zeta (2)=\pi ^2/6$

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