Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An asymptotic formula for the Taylor coefficients of automorphic forms


Author: Scott Wolpert
Journal: Proc. Amer. Math. Soc. 78 (1980), 485-491
MSC: Primary 10D15; Secondary 30F35
MathSciNet review: 556618
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An asymptotic estimate for the lattice of a Fuchsian group with quotient of finite area is discussed. The estimate is used to obtain an asymptotic formula for the Taylor coefficients of holomorphic automorphic forms.


References [Enhancements On Off] (What's this?)

  • [1] R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
  • [2] Tomio Kubota, Elementary theory of Eisenstein series, Kodansha Ltd., Tokyo; Halsted Press [John Wiley & Sons], New York-London-Sydney, 1973. MR 0429749
  • [3] W. K. Hayman, S. J. Patterson, and Ch. Pommerenke, On the coefficients of certain automorphic functions, Math. Proc. Cambridge Philos. Soc. 82 (1977), no. 3, 357–367. MR 0486496
  • [4] J. Lehner, Automorphic forms, Discrete groups and automorphic functions (Proc. Conf., Cambridge, 1975), Academic Press, London, 1977, pp. 73–120. MR 0492234
  • [5] S. J. Patterson, A lattice-point problem in hyperbolic space, Mathematika 22 (1975), no. 1, 81–88. MR 0422160
  • [6] S. J. Patterson, A footnote to: “On the coefficients of certain automorphic functions” (Math. Proc. Cambridge Philos. Soc. 82 (1977), no. 3, 357–367) by W. K. Hayman, Patterson and Ch. Pommerenke, Math. Proc. Cambridge Philos. Soc. 84 (1978), no. 2, 337–341. MR 0486497
  • [7] A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. (N.S.) 20 (1956), 47–87. MR 0088511

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 10D15, 30F35

Retrieve articles in all journals with MSC: 10D15, 30F35


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0556618-6
Article copyright: © Copyright 1980 American Mathematical Society