Counting zeros of Dedekind zeta functions

2021/02/09 by Hasanalizade, Elchin, Shen, Quanli, Wong, Peng-Jie · 1 citation
#11R42 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2102.04663

Abstract

Given a number field K of degree n_K and with absolute discriminant d_K, we obtain an explicit bound for the number N_K(T) of non-trivial zeros (counted with multiplicity), with height at most T, of the Dedekind zeta function ζ_K(s) of K. More precisely, we show that for T ≥ 1, | N_K (T) - \fracTπ log ( d_K ( (T)/(2πe))^n_K)| ≤ 0.228 (log d_K + n_K log T) + 23.108 n_K + 4.520, which improves previous results of Kadiri and Ng, and Trudgian. The improvement is based on ideas from the recent work of Bennett et al. on counting zeros of Dirichlet L-functions.

Cited by

• Estimating the number of zeros of Dedekind zeta-functions

Related

• Estimating the number of zeros of Dedekind zeta-functions
• On the lowest zero of Dedekind zeta function
• On density of the zeros of Dedekind zeta-functions
• New zero-free regions for Dedekind zeta-functions at small and large ordinates
• Number Field Analogue of Jacobi Theta Relation And Zeros of Dedekind zeta function on Re(s)=1/2