On real zeros of the Hurwitz zeta function

2023/05/10 by Karin Ikeda, Ikeda, Karin
Mathematics · #11M35 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2305.06107

openalex publication_date 2023/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we present results on the uniqueness of the real zeros of the Hurwitz zeta function in given intervals. The uniqueness in question, if the zeros exist, has already been proved for the intervals (0,1) and (-N, -N+1) for N ≥ 5 by Endo-Suzuki and Matsusaka respectively. We prove the uniqueness of the real zeros in the remaining intervals by examining the behavior of certain associated polynomials.

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