Abstract
One derives a refinement of the Wey1-Selberg asymptotic formula for an arbitrary Fuchsian group of the first kind with a noncompact fundamental domain.
Similar content being viewed by others
Literature cited
D. A. Hejhal, “The Selberg trace formula for PSL(2, R),” Vol. 1, Lect. Notes Math., No. 548, Springer-Verlag, Berlin (1976).
B. Randol, “The Riemann hypothesis for Selberg's zeta-function and the asymptotic behavior of eigenvalues of the Laplace operator,” Trans. Am. Math. Soc.,236, No. 513, 209–223 (1978).
A. Selberg, Harmonic Analysis. Part 2. Vorlesungsniederschrift, Göttingen (1954).
A. Selberg, “Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series,” J. Indian Math. Soc.,20, No. 1–3, 47–87 (1956).
T. Kubota, Elementary Theory of Eisenstein Series, Halsted Press, New York (1973).
L. D. Faddeev, “Expansion in eigenfunctions of the Laplace operator on the fundamental domain of a discrete group on the Lobachevskii plane,” Tr. Mosk. Mat. Obshch.,17, 323–349 (1967).
L. D. Faddeev, A. B. Venkov and V. L. Kalinin, “A nonarithmetic derivation of the Selberg formula,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,31, 5–42 (1973).
A. B. Venkov and A. I. Vinogradov, “The asymptotic distribution of the norms of hyperbolic classes and spectral characteristics of parabolic forms of weight zero for a Fuchsian group,” Dokl. Akad. Nauk SSSR,243, No. 6, 1373–1376 (1978).
E. C. Titchmarsh, The Theory of Functions, Oxford Univ. Press, Oxford (1939).
A. B. Venkov, “Selberg's trace formula for the Hecke operator generated by an involution,” Izv. Akad. Nauk SSSR, Ser. Mat.,42, No. 3, 484–499 (1978).
E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Clarendon Press, Oxford (1951).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 91, pp. 5–24, 1979.
Rights and permissions
About this article
Cite this article
Venkov, A.B. Remainder term in the Weyl-Selberg asymptotic formula. J Math Sci 17, 2083–2097 (1981). https://doi.org/10.1007/BF01567587
Issue Date:
DOI: https://doi.org/10.1007/BF01567587