Journal of the Mathematical Society of Japan

Joint universality for Lerch zeta-functions

Yoonbok LEE, Takashi NAKAMURA, and Łukasz PAŃKOWSKI

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For $0$ < $\alpha,$ $\lambda \leq 1$, the Lerch zeta-function is defined by $L(s;\alpha, \lambda) := \sum_{n=0}^\infty e^{2\pi i\lambda n} (n+\alpha)^{-s}$, where $\sigma$ > $1$. In this paper, we prove joint universality for Lerch zeta-functions with distinct $\lambda_1,\ldots,\lambda_m$ and transcendental $\alpha$.

Article information

J. Math. Soc. Japan, Volume 69, Number 1 (2017), 153-161.

First available in Project Euclid: 18 January 2017

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Digital Object Identifier

Primary: 11M35: Hurwitz and Lerch zeta functions

joint universality Lerch zeta-functions


LEE, Yoonbok; NAKAMURA, Takashi; PAŃKOWSKI, Łukasz. Joint universality for Lerch zeta-functions. J. Math. Soc. Japan 69 (2017), no. 1, 153--161. doi:10.2969/jmsj/06910153.

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