Improved estimates for the argument and zero-counting of Riemann zeta-function

2024/12/20 by Chiara Bellotti, Bellotti, Chiara, Peng‐Jie Wong +1 · 1 citation
Mathematics · #11M06 #11M26 (Primary) 11Y35 (Secondary) #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2412.15470

openalex publication_date 2024/12/20 · openalex created_date 2024/12/24 · openalex updated_date 2026/07/28

Abstract

In this article, we improve the recent work of Hasanalizade, Shen, and Wong by establishing | N (T) - (T)/( 2 π) log ( (T)/(2πe)) |≤ 0.10076log T+0.24460loglog T+8.08292 for every T≥ e, where N(T) is the number of non-trivial zeros ρ=β+iγ, with 0<γ≤ T, of the Riemann zeta-function ζ(s). The main source of improvement comes from implementing new subconvexity bounds for ζ(σ+it) on some σ_k-lines inside the critical strip.

Cited by

• Estimating the number of zeros of Dedekind zeta-functions

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