On real zeros of the Hurwitz zeta function

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.