Rationality of the Petersson Inner Product of Cohen's Kernels

Abstract

By explicitly calculating and then analytically continuing the Fourier expansion of the twisted double Eisenstein series $E_{s,k-s}^{\ast }(z,w;1/2)$ of Diamantis and O'Sullivan, we prove a formula of the Petersson inner product of Cohen's kernel and one of its twists, and obtain a rationality result. This extends a result of Kohnen and Zagier.