A note on Dedekind zeta values at 1/2

Abstract

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

Added comments from Professor J.-P. Serre in verbatim

Cited by in corpus (1)

• On quotients of derivatives of $L$-functions inside the critical strip