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

2018/03/06 by Ankush Goswami, Goswami, Ankush
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #History and Theory of Mathematics

paper · pdf · doi:10.48550/arxiv.1803.02467

Abstract

We provide a q-analogue of Euler's formula for ζ(2k) for k∈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 ζ(2)=π²/6 and ζ(4)=π⁴/90.

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