Hilbert Poincar\'e series and kernels for products of $L$-functions
- Resource Type
- Working Paper
- Authors
- Zhang, Mingkuan; Zhang, Yichao
- Source
- Subject
- Mathematics - Number Theory
- Language
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.