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An analogue of the Chowla-Selberg formula for several automorphic L-functions

Masatoshi Suzuki

math.NTarXiv:math/0606096

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 can be 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 Chowla-Selberg formula for Dirichlet L-functions and L-functions associated with 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 can be regarded as an analogue of Kronecker's limit formula.

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