Fixed points and conjugacy classes of regular elliptic elements in 𝑆𝑝(3,𝑍)

Eie, Min King; Lin, Chung Yuan

doi:10.1090/S0002-9947-1985-0784000-4

Fixed points and conjugacy classes of regular elliptic elements in $\textrm {Sp}(3,\textbf {Z})$
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Trans. Amer. Math. Soc. 289 (1985), 485-496 Request permission

Abstract:

In this paper, we obtain $13$ isolated fixed points (up to a $\operatorname {Sp}(3,{\mathbf {Z}})$-equivalence) and $86$ conjugacy classes of regular elliptic elements in $\operatorname {Sp}(3,{\mathbf {Z}})$. Hence the contributions from regular elliptic conjugacy classes in $\operatorname {Sp}(3,{\mathbf {Z}})$ to the dimension formula computed via the Selberg trace formula can be computed explictly by the main theorem of [${\mathbf {4}}$ or ${\mathbf {5}}$].

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