On density of the zeros of Dedekind zeta-functions

2022/03/16 by Wei Zhang, Zhang, Wei
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2203.08384

openalex publication_date 2022/03/16 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

For any σ with 0≤ σ≤ 1 and any T>10 sufficiently large, let N_ζ(σ,K,T) be the number of zeros ρ=β+iγ of ζ_K(s) with |γ|≤ T and β≥ σ and the zero being counted according to multiplicity. For k≥3, we have N_ζ(σ,K,T)≪ T^{(2k)/(6σ-3)(1-σ)+ε}, where (2k+3)/(2k+6)≤ σlt;1 and the implied constant may depend on the number field K and ε. This improves previous results for k≥3 of certain range of σ.

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