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 Es,k-s*(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.
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