Rationality of the Petersson Inner Product of Cohen's Kernels

Yuanyi You; Yichao Zhang

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arXiv · 2112.14164

Rationality of the Petersson Inner Product of Cohen's Kernels

Yuanyi You·Yichao Zhang

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Abstract

By explicitly calculating and then analytically continuing the Fourier expansion of the twisted double Eisenstein series $E_{s,k-s}^{*}(z,w; 1/2)$ 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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Yuanyi You, Yichao Zhang. 2021-12-28. Rationality of the Petersson Inner Product of Cohen's Kernels. https://arxiv.org/abs/2112.14164

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