Contributions from conjugacy classes of regular elliptic elements in 𝑆𝑝(𝑛,𝑍) to the dimension formula

Eie, Min King

doi:10.1090/S0002-9947-1984-0748846-X

Contributions from conjugacy classes of regular elliptic elements in $\textrm {Sp}(n, \textbf {Z})$ to the dimension formula
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by Min King Eie

Trans. Amer. Math. Soc. 285 (1984), 403-410

DOI: https://doi.org/10.1090/S0002-9947-1984-0748846-X

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Abstract:

The dimension of the space of cusp forms on the degree $n$ Siegel upper half-space can be obtained from the Selberg trace formula; in this paper we compute the contribution from the conjugacy classes of regular elliptic elements in $\operatorname {Sp}(n,{\mathbf {Z}})$ using Weyl’s character formula for representations of ${\text {GL}}(n,{\mathbf {C}})$.

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