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On the lowest zero of Dedekind zeta function (2401.10936v1)
Published 17 Jan 2024 in math.NT
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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