Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T06:40:11.201Z Has data issue: false hasContentIssue false
  • English
  • Français

On Some Dimension Formula for Automorphic Forms of Weight One, II

Published online by Cambridge University Press:  22 January 2016

Toyokazu Hiramatsu
Toyokazu Hiramatsu*
Affiliation:
Department of Mathematics Faculty of Science Kobe University, Nada-ku, Kobe 657, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let Γ be a fuchsian group of the first kind and assume that Γ contains the element and let x be a unitary representation of Γ of degree 1 such that X(—I) = — 1. Let S1(Γ,X) be the linear space of cusp forms of weight one on the group Γ with character X. We shall denote by d1 the dimension of the linear space S1(Γ, X). It is not effective to compute the number dl by means of the Riemann-Roch theorem. Because of this reason, it is an interesting problem in its own right to determine the number d1 by some other method (for example,).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 105 , March 1987 , pp. 169 - 186
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

References

[ 1 ] Hiramatsu, T., On some dimension formula for automorphic forms of weight one I, Nagoya Math. J., 85 (1982), 213–221.Google Scholar
[ 2 ] Jacquet, H. and Langlands, R. P., Automorphic forms on GL(2), Lecture Notes in Math., 114, Berlin, Heidelberg, New York: Springer 1970.Google Scholar
[ 3 ] Kubota, T., Elementary theory of Eisenstein series, Tokyo-New York: Kodansha and Halsted 1973.Google Scholar
[ 4 ] Selberg, A., Discontinuous groups and harmonic analysis, in Proc. International Math. Congr., Stockholm, 177–189, 1962.Google Scholar
[ 5 ] Serre, J.-P., Modular forms of weight one and Galois representations, in Proc. Symposium on Algebraic Number Fields, 193–268, London: Academic Press 1977.Google Scholar
[ 6 ] Hiramatsu, T., A formula for the dimension of spaces of cusp forms of weight one, to appear in Advanced Studies in Pure Math.Google Scholar