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VOL. 49 | 2007 An analogue of the Chowla–Selberg formula for several automorphic $L$-functions
Masatoshi Suzuki

Editor(s) Shigeki Akiyama, Kohji Matsumoto, Leo Murata, Hiroshi Sugita

## Abstract

In this paper, we will give a certain formula for the Riemann zeta function that expresses the Riemann zeta function by an infinte series consisting of $K$-Bessel functions. Such an infinite series expression is regarded as an analogue of the Chowla-Selberg formula. Roughly speaking, the Chowla-Selberg formula is the formula that expresses the Epstein zeta-function by an infinite series consisting of $K$-Bessel functions. In addition, we also give certain analogues of the Chawla-Selberg formula for Dirichlet $L$-functions and $L$-functions attached to holomorphic cusp forms. Moreover, we introduce a two variable function which is analogous to the real analytic Eisenstein series and give a certain limit formula for this one. Such a limit formula is regarded as an analogue of Kronecker's limit formula.

## Information

Published: 1 January 2007
First available in Project Euclid: 27 January 2019

zbMATH: 1219.11137
MathSciNet: MR2405616

Digital Object Identifier: 10.2969/aspm/04910479

Subjects:
Primary: 11M06
Secondary: 11F66, 11F67, 11M20, 11M41

Rights: Copyright © 2007 Mathematical Society of Japan

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Vol. 49 • 1 January 2007