Rankin-Cohen Brackets of Hilbert Hecke Eigenforms
Number Theory
2024-05-29 v1
Abstract
Over any fixed totally real number field with narrow class number one, we prove that the Rankin-Cohen bracket of two Hecke eigenforms for the Hilbert modular group can only be a Hecke eigenform for dimension reasons, except for a couple of cases where the Rankin-Selberg method does not apply. We shall also prove a conjecture of Freitag on the volume of Hilbert modular groups, and assuming a conjecture of Freitag on the dimension of the cuspform space, we obtain a finiteness result on eigenform product identities.
Keywords
Cite
@article{arxiv.2405.17887,
title = {Rankin-Cohen Brackets of Hilbert Hecke Eigenforms},
author = {Yichao Zhang and Yang Zhou},
journal= {arXiv preprint arXiv:2405.17887},
year = {2024}
}