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Agmon's complex Tauberian theorem and closed orbits for hyperbolic and geodesic flows
Author:
Mark Pollicott
Journal:
Proc. Amer. Math. Soc. 114 (1992), 1105-1108
MSC:
Primary 58F20; Secondary 11M45, 58F17
MathSciNet review:
1045147
Full-text PDF Free Access
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Abstract: In this note we give an alternative proof of Sharp's dynamical analogue of Merten's theorem for hyperbolic flows. Our use of a tauberian theorem of Agmon also allows us to get better error terms.
- [1]
George
Arfken, Mathematical methods for physicists, Academic Press,
New York-London, 1966. MR 0205512
(34 #5339)
- [2]
Shmuel
Agmon, Complex variable Tauberians,
Trans. Amer. Math. Soc. 74 (1953), 444–481. MR 0054079
(14,869a), http://dx.doi.org/10.1090/S0002-9947-1953-0054079-5
- [3]
William
Parry, Bowen’s equidistribution theory and the Dirichlet
density theorem, Ergodic Theory Dynam. Systems 4
(1984), no. 1, 117–134. MR 758898
(86j:58125), http://dx.doi.org/10.1017/S0143385700002315
- [4]
William
Parry and Mark
Pollicott, An analogue of the prime number theorem for closed
orbits of Axiom A flows, Ann. of Math. (2) 118
(1983), no. 3, 573–591. MR 727704
(85i:58105), http://dx.doi.org/10.2307/2006982
- [5]
Richard
Sharp, An analogue of Mertens’ theorem for closed orbits of
Axiom A flows, Bol. Soc. Brasil. Mat. (N.S.) 21
(1991), no. 2, 205–229. MR 1139566
(93a:58142), http://dx.doi.org/10.1007/BF01237365
- [6]
A. Verkov, Spectral theory of automorphic functions, the Selberg zeta function, and some problems of analytic number theory, Russian Math. Surv. 34 (1979), 79-153.
- [1]
- G. Arfken, Mathematical methods for physicists, Academic Press, New York, 1970. MR 0205512 (34:5339)
- [2]
- S. Agmon, Complex variable tauberians, Trans. Amer. Math. Soc. 74 (1953), 444-481. MR 0054079 (14:869a)
- [3]
- W. Parry, Bowen's equidistribution theory and the Dirichlet density theorem, Ergodic Theory Dynamical Systems 4 (1984), 117-134. MR 758898 (86j:58125)
- [4]
- W. Parry and M. Pollicott, An analogue of the prime orbit theorem for closed orbits of Axiom A flows, Ann. of Math. 118 (1983), 573-591. MR 727704 (85i:58105)
- [5]
- R. Sharp, An analogue of Mertens' theorem for closed orbits of Axiom A flows, preprint, Warwick University. MR 1139566 (93a:58142)
- [6]
- A. Verkov, Spectral theory of automorphic functions, the Selberg zeta function, and some problems of analytic number theory, Russian Math. Surv. 34 (1979), 79-153.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1992-1045147-X
PII:
S 0002-9939(1992)1045147-X
Article copyright:
© Copyright 1992
American Mathematical Society
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