Rankin-Cohen Brackets of Hilbert Hecke Eigenforms
Research Square (Research Square)(2024)
摘要
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.
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