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arXiv · 2401.10936

On the lowest zero of Dedekind zeta function

Sushant Kala
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Abstract

Let $\zeta_K(s)$ denote the Dedekind zeta-function associated to a number field $K$. In this paper, we give an effective upper bound for the height of first non-trivial zero other than $1/2$ of $\zeta_K(s)$ under the generalized Riemann hypothesis. This is a refinement of the earlier bound obtained by Omar Sami.

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Sushant Kala. 2024-01-17. On the lowest zero of Dedekind zeta function. https://doi.org/10.1017/s000497272400090x

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