New zero-free regions for Dedekind zeta-functions at small and large ordinates

2025/06/24 by Das, Sourabhashis, Swati Gaba, Gaba, Swati +6 · 1 citation
Mathematics · #11R42 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2506.19319

openalex publication_date 2025/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a number field L≠ ℚ, we obtain new and explicit zero-free regions for Dedekind zeta-functions of L, which refine the previous works of Ahn--Kwon, Kadiri, and Lee. In particular, for low-lying zeros, we extend Kadiri's result to all number fields while improving the main constant.

Citations

• Explicit zero-free regions for the Riemann zeta-function
• Primes in the Chebotarev density theorem for all number fields
• An explicit upper bound for the least prime ideal in the Chebotarev\n density theorem
• Nonnegative trigonometric polynomials and a zero-free region for the Riemann zeta-function
• Numerical Computations Concerning the GRH
• On the zeros of the Riemann Zeta function
• Über die Nullstellen der Riemannschen Zetafunktion

Cited by

• Explicit zero-free regions for automorphic L-functions

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• Zeros of partial sums of the Dedekind zeta function of a cyclotomic\n field