Journal of the Mathematical Society of Japan

Functional distribution for a collection of Lerch zeta functions

Hidehiko MISHOU

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Let 0 < $\alpha$ < 1 be a transcendental real number and $\lambda_1,\ldots,\lambda_r$ be real numbers with $0 \le \lambda_j$ < 1. It is conjectured that a joint universality theorem for a collection of Lerch zeta functions $\{L(\lambda_j,\alpha,s)\}$ will hold for every numbers $\lambda_j$'s which are different each other. In this paper we will prove that the joint universality theorem for the set $\{L(\lambda_j,\alpha,s)\}$ holds for almost all real numbers $\lambda_j$'s.

Article information

J. Math. Soc. Japan, Volume 66, Number 4 (2014), 1105-1126.

First available in Project Euclid: 23 October 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11M35: Hurwitz and Lerch zeta functions
Secondary: 11M06: $\zeta (s)$ and $L(s, \chi)$ 11K38: Irregularities of distribution, discrepancy [See also 11Nxx]

Lerch zeta function joint universality theorem discrepancy


MISHOU, Hidehiko. Functional distribution for a collection of Lerch zeta functions. J. Math. Soc. Japan 66 (2014), no. 4, 1105--1126. doi:10.2969/jmsj/06641105.

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