Contributions from conjugacy classes of regular elliptic elements in Hermitian modular groups to the dimension formula of Hermitian modular cusp forms

Author:
Min King Eie

Journal:
Trans. Amer. Math. Soc. **294** (1986), 635-645

MSC:
Primary 11F46; Secondary 11F55, 11F72, 32N15

DOI:
https://doi.org/10.1090/S0002-9947-1986-0825727-6

MathSciNet review:
825727

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Abstract: The dimension of the vector space of hermitian modular cusp forms on the hermitian upper half plane can be obtained from the Selberg trace formula; in this paper we shall compute the contributions from conjugacy classes of regular elliptic elements in hermitian modular groups by constructing an orthonomal basis in a certain Hilbert space of holomorphic functions. A generalization of the main Theorem can be applied to the dimension formula of cusp forms of $SU(p, q)$. A similar theorem was given for the case of regular elliptic elements of ${\text {Sp}}(n, {\mathbf {Z}})$ in [**5**] via a different method.

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Article copyright:
© Copyright 1986
American Mathematical Society