Sarnak, Peter Asymptotic behavior of periodic orbits of the horocycle flow and Eisenstein series. (English) Zbl 0501.58027 Commun. Pure Appl. Math. 34, 719-739 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 53 Documents MSC: 37A99 Ergodic theory 30F99 Riemann surfaces 28D10 One-parameter continuous families of measure-preserving transformations 37C10 Dynamics induced by flows and semiflows 37G99 Local and nonlocal bifurcation theory for dynamical systems 11M06 \(\zeta (s)\) and \(L(s, \chi)\) Keywords:non-compact Riemann surface; horocycle flow; invariant probability measure; flow-invariant distributions; Riemannian measure; geodesic flows; modular group PDF BibTeX XML Cite \textit{P. Sarnak}, Commun. Pure Appl. Math. 34, 719--739 (1981; Zbl 0501.58027) Full Text: DOI OpenURL References: [1] Bowen, Amer. J. Math. 94 pp 413– (1972) [2] and , Notes on Selberg’s trace formula, to appear. · Zbl 0325.22014 [3] Dani, Bull. Amer. Math. Soc. 3 pp 1037– (1980) [4] Advances in Topological Dynamics, Springer Lecture Notes in Math. No. 318, pp. 95–114. [5] Hedlund, Duke Math. J. 2 pp 530– (1936) [6] Elementary Theory of Eisenstein Series, Halsted Press, 1973. · Zbl 0268.10012 [7] Lax, Ann. of Math. 87 (1976) [8] Selberg, J. Indian Math. Soc. 20 pp 47– (1956) [9] The Theory of the Riemann Zeta Function, Oxford, 1951. [10] Eisenstein series and the Riemann zeta function, to appear. · Zbl 0484.10019 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.