Location of Repository

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 Sp(n, Z) in [5J via a different method. 1. Introduction and notation. Denote by E the unit matrix and by 0 the zero matrix in the matrix ring Mn(C). Put J = [_DE~] ' The hermitian symplectic group of degree n, On, is then defined as the group of matrices in M2n (C); it satisfies tMJM = J; i.e. On = {M E M2n(c)1 tMJM = J}

Year: 2013

OAI identifier:
oai:CiteSeerX.psu:10.1.1.309.1812

Provided by:
CiteSeerX

Download PDF:To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.