On the lowest zero of Dedekind zeta function

2024/01/17 by Sushant Kala, Kala, Sushant
Mathematics · #11M26 #11R42 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2401.10936

openalex publication_date 2024/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let ζ_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 ζ_K(s) under the generalized Riemann hypothesis. This is a refinement of the earlier bound obtained by Omar Sami.

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