2006/06/05 by Masatoshi Suzuki, Suzuki, Masatoshi
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #math.NT #msc:11M06 #msc:11M20
paper · pdf · doi:10.48550/arxiv.math/0606096
23 pages, 2 figures
arxiv created 2006/06/05 · arxiv updated 2009/12/01
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.