Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-27T21:40:07.839Z Has data issue: false hasContentIssue false
  • English
  • Français

The square mean of Dirichlet series associated with cusp forms

Published online by Cambridge University Press:  26 February 2010

Anton Good
Anton Good
Affiliation:
Forschungsinstitut für Mathematik, ETH-Zentrum, CH-8092 Zürich, Switzerland
Get access

Extract

Let

be a cusp form of even integral weight k > 2 for the full modular group. Then the Dirichlet series

is absolutely convergent for σ > ½(k + 1). Hecke showed that LF is an entire function of s satisfying the functional equation

Type
Research Article
Information
Mathematika , Volume 29 , Issue 2 , December 1982 , pp. 278 - 295
Copyright
Copyright © University College London 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Good, A.. Approximative Funktionalgleichungen und Mittelwertsatze fiir Dirichletreihen, die Spitzenformen assoziiert sind. Cotnm. Math. Helv., 50 (1975), 327–361.CrossRefGoogle Scholar
2.Good, A.. Beiträge zur Theorie der Dirichletreihen, die Spitzenformen zugeordnet sind. J. Number Theory, 13 (1981), 18–65.CrossRefGoogle Scholar
3.Good, A.. Cusp forms and eigenfunctions of the Laplacian. Math. Ann., 225 (1981), 523–548.Google Scholar
4.Good, A.. Local analysis of Selberg's trace formula. (To appear.)Google Scholar
5.Iwaniec, H.. Fourier coefficients of cusp forms and the Riemann zeta-function. Bordeaux Sém. Théorie des Nombres, exp. no. 18. (1979/1980), 1–36.Google Scholar
6.Kubota, T.. Elementary theory of Eisenstein series (Kodansha, Tokyo, 1973).Google Scholar
7.Magnus, W., Oberhettinger, F. and Soni, R. P.. Formulas and theorems for the special functions of mathematical physics (Springer, Berlin, 3rd ed., 1966).CrossRefGoogle Scholar
8.Roelcke, W.. Ueber die Wellengleichung bei Grenzkreisgruppen erster Art. S.B. Heidelberger Akad. Wiss. Math. Nat. Kl. 4. Abh. (1956), 159–267.CrossRefGoogle Scholar
9.Titchmarsh, E. C.. The theory of the Riemann zeta-function (Oxford, 1951).Google Scholar