Some topics related to universality of L-functions with an Euler product

Takashi Nakamura

doi:10.1524/anly.2011.1077

Article

Some topics related to universality of L-functions with an Euler product

Takashi Nakamura

Published/Copyright: January 18, 2011

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From the journal Analysis Volume 31 Issue 1

Abstract

In this paper, we show the joint universality of the set of the Steuding class L-functions {L(s+iδ_lτ)}_l=1^m for almost all (δ₁,…,δ_m)∈R^m. From this property, we obtain the result that {L(s+iδ_lτ)}_l=j,k, where δ_j and δ_k are two of the above, has a kind of generalized strong recurrence. Roughly speaking, this means that L(s+iδ_jτ) can be uniformly approximated by L(s+iδ_kτ) in the sense of universality. Moreover, we consider the relation between the generalized strong recurrence and zeros of the Selberg and Steuding class L-functions L(s). Finally, we obtain the upper bound for the density of universality for the Steuding class L-functions.

Keywords: joint universality; $L$-functions; Riemann hypothesis; Selberg class; Steuding class

^* Correspondence address: Tokyo University of Science, Department of Mathematics, Faculty of Science and Technology, Noda, CHIBA 278-8510, Japan, nakamura takashi@ma.noda.tus.ac.jp

Published Online: 2011-01-18

Published in Print: 2011-01-01

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Articles in the same Issue

https://doi.org/10.1524/anly.2011.1077

Keywords for this article

joint universality; $L$-functions; Riemann hypothesis; Selberg class; Steuding class