A $q$-analogue for Euler's evaluations of the Riemann zeta function

Ankush Goswami

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arXiv · 1803.02467

A $q$-analogue for Euler's evaluations of the Riemann zeta function

Ankush Goswami

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Abstract

We provide a $q$-analogue of Euler's formula for $\zeta(2k)$ for $k\in\mathbb{Z}^+$. Our main results are stated in Theorems 3.1 and 3.2 below. The result generalizes a recent result of Z.W. Sun who obtained $q$-analogues of $\zeta(2)=\pi^2/6$ and $\zeta(4)=\pi^4/90$.

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Ankush Goswami. 2018-03-06. A $q$-analogue for Euler's evaluations of the Riemann zeta function. https://arxiv.org/abs/1803.02467

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