The loxodromic term of the Selberg trace formula for
Author:
D. I. Wallace
Journal:
Proc. Amer. Math. Soc. 113 (1991), 59
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 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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Y. Efrat, The Selberg trace formula for
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Math. Soc. 65 (1987), no. 359, iv+111. MR 874084
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Douglas
Grenier, Fundamental domains for the general linear group,
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0429749 (55 #2759)
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A. B. Venkov, The Selberg trace formula for , Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 37 (1973).
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D.
I. Wallace, Conjugacy classes of hyperbolic
matrices in 𝑆𝑙(𝑛,𝑍) and ideal classes in an
order, Trans. Amer. Math. Soc.
283 (1984), no. 1,
177–184. MR
735415 (85h:11024), http://dx.doi.org/10.1090/S00029947198407354150
 [6]
D.
I. Wallace, Explicit form of the hyperbolic term in the Selberg
trace formula for 𝑆𝑙(3,𝑍) and Pell’s equation
for hyperbolics in 𝑆𝑙(3,𝑍), J. Number Theory
24 (1986), no. 2, 127–133. MR 863649
(88c:11029), http://dx.doi.org/10.1016/0022314X(86)900971
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D.
I. Wallace, Terms in the Selberg trace formula for
𝑆𝐿(3,𝑍)\𝑆𝐿(3,𝑅)/𝑆𝑂(3,𝑅)
associated to Eisenstein series coming from a maximal parabolic
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106 (1989), no. 4,
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 [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), 293317. 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), 177183. 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), 127133. 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), 875883. MR 963577 (90e:11081)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199110874733
PII:
S 00029939(1991)10874733
Article copyright:
© Copyright 1991 American Mathematical Society
