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arXiv · 1705.08102

Real zeros of Hurwitz zeta-functions and their asymptotic behavior in the interval $(0,1)$

Kenta Endo·Yuta Suzuki
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Abstract

Let $0<a\leq1, s\in\mathbb{C}$, and $ζ(s,a)$ be the Hurwitz zeta-function. Recently, T.~Nakamura showed that $ζ(σ,a)$ does not vanish for any $0<σ<1$ if and only if $1/2\leq a \leq1$. In this paper, we show that $ζ(σ,a)$ has precisely one zero in the interval $(0,1)$ if $0<a<1/2$. Moreover, we reveal the asymptotic behavior of this unique zero with respect to $a$.

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Kenta Endo, Yuta Suzuki. 2017-05-23. Real zeros of Hurwitz zeta-functions and their asymptotic behavior in the interval $(0,1)$. https://arxiv.org/abs/1705.08102

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