Pullbacks of Siegel Eisenstein Series and Weighted Averages of Critical $L$-values

Abstract

In this paper we obtain a weighted average formula for special values of $L$-functions attached to normalized elliptic modular forms of weight $k$ and full level. These results are obtained by studying the pullback of a Siegel Eisenstein series and working out an explicit spectral decomposition.

12 pages

References in corpus (1)

• On the cuspidality of pullbacks of Siegel Eisenstein series and applications to the Bloch-Kato conjecture