Hilbert Poincar\'e series and kernels for products of $L$-functions
Number Theory
2024-01-03 v1
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.
Keywords
Cite
@article{arxiv.2401.01282,
title = {Hilbert Poincar\'e series and kernels for products of $L$-functions},
author = {Mingkuan Zhang and Yichao Zhang},
journal= {arXiv preprint arXiv:2401.01282},
year = {2024}
}