Siegfried Böcherer (Universität Mannheim): Is there an analogue of Clausen-von Staudt for special values of automorphic $L$-functions?

A weak version of Clausen von Staudt says that generalized Bernoulli numbers $B_{n,\chi}$ have bounded denominators, when $\chi$ varies over Dirichlet characters. One can ask the same question for critical values of $L$-functions attached to modular forms, but there seem to be no results on this in the literature. We will give an affirmative answer in the case of standard $L$-functions for Siegel modular forms. The main tool is an integral representation of such $L$-functions using Eisenstein series.