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Analogues of the Artin factorization formula for the automorphic scattering matrix and Selberg zeta-function associated to a Kleinian group
Author(s):
Joshua
S.
Friedman
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3395-3404.
MSC (2000):
Primary 11F72
Posted:
June 10, 2008
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Abstract:
For Kleinian groups acting on a hyperbolic three-space, we prove factorization formulas for both the Selberg zeta-function and the automorphic scattering matrix. We extend results of Venkov and Zograf from Fuchsian groups to Kleinian groups, and we give a proof that is simple and extendable to more general groups.
References:
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- J. Elstrodt, F. Grunewald, and J. Mennicke, Groups acting on hyperbolic space, Harmonic analysis and number theory, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1998. MR 1483315 (98g:11058)
- [Fri05a]
- Joshua S. Friedman, The Selberg trace formula and Selberg zeta-function for cofinite Kleinian groups with finite-dimensional unitary representations, Math. Z. 250 (2005), no. 4, 939-965. MR 2180383 (2006g:11099)
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- -, The Selberg trace formula and Selberg zeta-function for cofinite Kleinian groups with finite-dimensional unitary representations. Ph.D. Thesis, Stony Brook University, 2005, http://arxiv.org/abs/math.NT/0612807.
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- Dennis A. Hejhal, The Selberg trace formula for
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- A. B. Venkov, Spectral theory of automorphic functions, Proc. Steklov Inst. Math. 1982, no. 4(153) (1983); a translation of Trudy Mat. Inst. Steklov. 153 (1981). MR 665585 (85j:11060a), MR 0692019 (85j:11060b)
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- A. B. Venkov and P. G. Zograf, Analogues of Artin's factorization formulas in the spectral theory of automorphic functions associated with induced representations of Fuchsian groups, Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), 1150-1158, 1343; translated in Math. USSR-Izvestiya 21 (1983), no. 3, 435-443. MR 0682487 (85f:11041)
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Additional Information:
Joshua
S.
Friedman
Affiliation:
Department of Mathematics and Sciences, United States Merchant Marine Academy, 300 Steamboat Road, Kings Point, New York 11024
Email:
CrownEagle@gmail.com, friedmanj@usmma.edu, joshua@math.sunysb.edu
DOI:
10.1090/S0002-9939-08-09516-6
PII:
S 0002-9939(08)09516-6
Received by editor(s):
March 2, 2007
Posted:
June 10, 2008
Communicated by:
Wen-Ching Winnie Li
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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