Contributions from conjugacy classes of regular elliptic elements in Hermitian modular groups to the dimension formula of Hermitian modular cusp forms
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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.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- 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