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

2017/05/23 by Kenta Endo, Yuta Suzuki, Endo, Kenta +1
Mathematics · #11M20(Secondary) #11M35(Primary) #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1705.08102

5pages

arxiv created 2017/05/23 · arxiv updated 2017/05/24

Abstract

Let 0<a≤1, s∈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≤ a ≤1. 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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