An analogue of the Chowla—Selberg formula forseveral automorphic L-functions

摘要

In this paper, we will give a certain formula for the Riemann zetafunction that expresses the Riemann zeta function by an infinte se-ries consisting of K-Bessel functions. Such an infinite series expressionis regarded as an analogue of the Chowla-Selberg formula. Roughlyspeaking, the Chowla-Selberg formula is the formula that expressesthe Epstein zeta-function by an infinite series consisting of K-Besselfunctions. In addition, we also give certain analogues of the Chowla-Selberg formula for Dirichlet L-functions and L-functions attached toholomorphic cusp forms. Moreover, we introduce a two variable func-tion which is analogous to the real analytic Eisenstein series and givea certain limit formula for this one. Such a limit formula is regardedas an analogue of Kronecker's limit formula.