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The existence and the non-existence of joint t-universality for Lerch zeta functions

✍ Scribed by Takashi Nakamura

Publisher: Elsevier Science
Year: 2007
Tongue: English
Weight: 191 KB
Volume: 125
Category: Article
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2006.12.008

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✦ Synopsis

In this paper, we show the following theorems. Suppose 0 < a l < 1 are algebraically independent numbers and 0 < λ l 1 for 1 l m. Then we have the joint t-universality for Lerch zeta functions L(λ l , a l , s) for 1 l m. Next we generalize Lerch zeta functions, and obtain the joint t-universality for them. In addition, we show examples of the non-existence of the joint t-universality for Lerch zeta functions and generalized Lerch zeta functions.

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