Hilbert Poincar\'e series and kernels for products of $L$-functions

Mingkuan Zhang; Yichao Zhang

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arXiv · 2401.01282

Hilbert Poincar\'e series and kernels for products of $L$-functions

Mingkuan Zhang·Yichao Zhang

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Abstract

We study Hilbert Poincar\'e series associated to general seed functions and construct Cohen's kernels and double Eisenstein series as series of Hilbert Poincar\'e series. Then we calculate the Rankin-Cohen brackets of Hilbert Poincar\'e series and Hilbert modular forms and extend Zagier's kernel formula to totally real number fields. Finally, we show that the Rankin-Cohen brackets of two different types of Eisenstein series are special values of double Eisenstein series up to a constant.

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Mingkuan Zhang, Yichao Zhang. 2024-01-02. Hilbert Poincar\'e series and kernels for products of $L$-functions. https://arxiv.org/abs/2401.01282

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