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The joint universality and the functional independence for Lerch zeta-functions

Published online by Cambridge University Press:  22 January 2016

Antanas Laurinčikas  and
Kohji Matsumoto
Antanas Laurinčikas
Affiliation:
Department of Mathematics, Vilnius University, Naugarduko, 24, 2006 Vilnius, Lithuania, [email protected]
Kohji Matsumoto
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602, Japan, [email protected]
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Abstract

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The joint universality theorem for Lerch zeta-functions L(λl, αl, s) (1 ≤ l ≤ n) is proved, in the case when λls are rational numbers and αls are transcendental numbers. The case n = 1 was known before ([12]); the rationality of λls is used to establish the theorem for the “joint” case n ≥ 2. As a corollary, the joint functional independence for those functions is shown.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 157 , 2000 , pp. 211 - 227
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2000

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