The loxodromic term of the Selberg trace formula for 𝑆𝐿(3,𝑍)\𝑆𝐿(3,𝑅)/𝑆𝑂(3,𝑅)

Wallace, D. I.

doi:10.1090/S0002-9939-1991-1087473-3

The loxodromic term of the Selberg trace formula for $\textrm {SL}(3,\textbf {Z})\backslash \textrm {SL}(3,\textbf {R})/\textrm {SO}(3,\textbf {R})$
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Proc. Amer. Math. Soc. 113 (1991), 5-9 Request permission

Abstract:

In this paper we calculate the contribution to the trace formula of those orbital integrals coming from matrices in $\operatorname {SL} (3,\mathbb {Z})$ with two complex eigenvalues and one real one, none of which are equal to zero. These correspond to mixed cubic number fields and will be seen to occur with multiplicity equal to the class number of a certain order in the number field.

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The Selberg trace formula for

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