Kernels of $L$-functions of cusp forms

Nikolaos Diamantis, Cormac O'Sullivan

Published 2009-04-14, updated 2009-08-18Version 2

We give a new expression for the inner product of two kernel functions associated to a cusp form. Among other applications, it yields an extension of a formula of Kohnen and Zagier, and another proof of Manin's Periods Theorem. Cohen's representation of these kernels as series is also generalized.