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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:473

Article

Endo, Kenta¹  Suzuki, Yuta¹ 

[1] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan

关键词: Hurwitz zeta-function;    Real zeros;   

DOI  :  10.1016/j.jmaa.2018.12.001

来源: Elsevier

【 摘 要 】

Let 0 < a <= 1, s epsilon C, and zeta(s, a) be the Hurwitz zeta-function. Recently, Nakamura showed that zeta(sigma, a) does not vanish for any 0 < sigma < 1 if and only if 1/2 <= a <= 1. In this paper, we show that zeta(sigma, 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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free