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On the relative distribution of eigenvalues of exceptional Hecke operators and automorphic Laplacians
Author(s):
E.
Balslev;
A.
Venkov
Original publication:
Algebra i Analiz,
tom 17
(2005),
vypusk 1.
Journal:
St. Petersburg Math. J.
17
(2006),
1-37.
MSC (2000):
Primary 11F72
Posted:
January 19, 2006
MathSciNet review:
2140673
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References |
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Additional information
Abstract:
The relative distribution of the embedded eigenvalues of exceptional Hecke operators and automorphic Laplacians is studied in connection with the Phillips and Sarnak conjectures concerning the violation of the Weyl law.
References:
-
- 1.
- E. Balslev and A. Venkov, Spectral theory of Laplacians for Hecke groups with primitive character, Acta Math. 186 (2001), 155-217. MR 1846029 (2002f:11057)
- 2.
- A. Venkov, Spectral theory of automorphic functions, Trudy Mat. Inst. Steklov. 153 (1981), 172 pp.; English transl., Proc. Steklov Inst. Math. 1982, no. 4 (153), 163 pp. MR 0665585 (85j:11060a); MR 0692019 (85j:11060b)
- 3.
- S. Akiyama and Y. Tanigawa, The Selberg trace formula for modular correspondences, Nagoya Math. J. 117 (1990), 93-123. MR 1044938 (91c:11028)
- 4.
- D. A. Hejhal, The Selberg trace formula for
 . Vol. 2, Lecture Notes in Math., vol. 1001, Springer-Verlag, Berlin, 1983. MR 0711197 (86e:11040) - 5.
- A. Strömbergsson, The Selberg trace formula for modular correspondences, Licentiate thesis, Uppsala Univ., 1998 (http://www.math.uu.se/~andreas/papers.html).
- 6.
- J. B. Conrey and Lie Xian-Jin, On the trace of Hecke operators for Maass forms for congruence subgroups
 , Preprint (http://www.math.byu.edu/~xianjin/papers.html). - 7.
- J. Bolte and C. Grosche, Selberg trace formula for bordered Riemann surfaces, Comm. Math. Phys. 163 (1994), 217-244. MR 1284783 (95g:11087)
- 8.
- L. Faddeev, The eigenfunction expansion of Laplace's operator on the fundamental domain of a discrete group on the Lobachevskii plane, Trudy Moskov. Mat. Obshch. 17 (1967), 323-350; English transl. in Trans. Moscow Math. Soc. 17 (1969). MR 0236768 (38:5062)
- 9.
- W. Luo, Nonvanishing of
 -values and the Weyl law, Ann. of Math. (2) 154 (2001), 477-502. MR 1865978 (2002i:11084) - 10.
- E. Balslev and A. Venkov, Correction to ``Spectral theory of Laplacians for Hecke groups with primitive character", Acta Math. 192 (2004), 1-3. MR 2079596 (2005d:11077)
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Additional Information:
E.
Balslev
Affiliation:
Department of Mathematical Sciences, University of Aarhus, Denmark
Email:
balslev@imf.au.dk
A.
Venkov
Affiliation:
Department of Mathematical Sciences, University of Aarhus, Denmark
Email:
venkov@imf.au.dk
DOI:
10.1090/S1061-0022-06-00891-0
PII:
S 1061-0022(06)00891-0
Keywords:
Selberg trace formula,
Weyl law,
Phillips and Sarnak conjectures
Received by editor(s):
7/SEP/2004
Posted:
January 19, 2006
Dedicated:
Dedicated to Ludwig Faddeev on the occasion of his seventieth birthday
Copyright of article:
Copyright
2006,
American Mathematical Society
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