The loxodromic term of the Selberg trace formula for

Author:
D. I. Wallace

Journal:
Proc. Amer. Math. Soc. **113** (1991), 5-9

MSC:
Primary 11F72; Secondary 22E46

DOI:
https://doi.org/10.1090/S0002-9939-1991-1087473-3

MathSciNet review:
1087473

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we calculate the contribution to the trace formula of those orbital integrals coming from matrices in 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.

**[1]**Isaac Efrat,*The Selberg trace formula for*, Mem. Amer. Math. Soc., no. 65, Amer. Math. Soc., Providence, RI, 1987. MR**874084 (88e:11041)****[2]**Doug Grenier,*Fundamental domains for the general linear group*, Pacific J. Math.**132**(1988), 293-317. MR**934172 (89d:11055)****[3]**T. Kubota,*Elementary theory of Eisenstein series*, Kodansha Ltd., 1973. MR**0429749 (55:2759)****[4]**A. B. Venkov,*The Selberg trace formula for*, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI)**37**(1973).**[5]**D. I. Wallace,*Conjugacy classes of hyperbolic matrices in**and ideal classes in an order*, Trans. Amer. Math. Soc.**283**(1984), 177-183. MR**735415 (85h:11024)****[6]**-,*Explicit form of the hyperbolic term in the Selberg trace formula for**and Pell's equation for hyperbolics in*, J. Number Theory**24**(1986), 127-133. MR**863649 (88c:11029)****[7]**-,*Terms in the Selberg trace formula for**associated to Eisenstein series coming from a maximal parabolic subgroup*, Proc. Amer. Math. Soc.**106**(1989), 875-883. MR**963577 (90e:11081)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
11F72,
22E46

Retrieve articles in all journals with MSC: 11F72, 22E46

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1087473-3

Article copyright:
© Copyright 1991
American Mathematical Society