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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The loxodromic term of the Selberg trace formula for $ {\rm SL}(3,{\bf Z})\backslash{\rm SL}(3,{\bf R})/{\rm SO}(3,{\bf R})$


Author: D. I. Wallace
Journal: Proc. Amer. Math. Soc. 113 (1991), 5-9
MSC: Primary 11F72; Secondary 22E46
MathSciNet review: 1087473
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1087473-3
PII: S 0002-9939(1991)1087473-3
Article copyright: © Copyright 1991 American Mathematical Society