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arXiv · 2212.00324

A note on Dedekind zeta values at 1/2

Neelam Kandhil
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Abstract

For a number field $K$, let $ζ_{K}(s)$ be the Dedekind zeta function associated to $K$. In this note, we study non-vanishing and transcendence of $ζ_{K}$ as well as its derivative $ζ_{K}'$ at $s= 1/2$. En route, we strengthen a result proved by Ram Murty and Tanabe [On the nature of $e^γ$ and non-vanishing of $L$-series at $s= 1/2$, J. Number Theory 161 (2016) 444-456].

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Neelam Kandhil. 2022-12-12. A note on Dedekind zeta values at 1/2. https://doi.org/10.1142/s1793042122500658

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