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On real zeros of the Hurwitz zeta function

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Speaker: 
Karin Ikeda
Affiliation: 
Kyushu University
Date: 
Fri, 15/09/2023 - 10:50 - 11:10
Location: 
MPIM Lecture Hall

In this talk, I will present a solution to the problem of real zeros of the Hurwitz zeta function, which has remained unsolved in previous studies. After reviewing the works of Spira, Nakamura, Matsusaka, and Endo-Suzuki, I discuss the remaining case, namely the zeros in the interval $(-4, 0)$. This work shows that all real zeros of the Hurwitz zeta function, like the Riemann zeta function, are simple. I also present an observation of a curious behavior of a family of polynomials used in the proof.

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