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On some dimension formula for automorphic forms of weight one III

Published online by Cambridge University Press:  22 January 2016

Toyokazu Hiramatsu  and
Shigeki Akiyama
Toyokazu Hiramatsu
Affiliation:
Department of Mathematics, Faculty of Science, Kobe University, Rokko, 657, Japan
Shigeki Akiyama
Affiliation:
Department of Mathematics, Faculty of Science, Kobe University, Rokko, 657, Japan
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Let Γ be a fuchsian group of the first kind and assume that Γ does not contain the element . Let S1(Γ) be the linear space of cusp forms of weight 1 on the group Γ and denote by d1 the dimension of the space S1(Γ). When the group Γ has a compact fundamental domain, we have obtained the following (Hiramatsu [3]):

(*) ,

where ς*(s) denotes the Selberg type zeta function defined by

.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 111 , September 1988 , pp. 157 - 163
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1988

References

[1] Hiramatsu, T., On some dimension formula for automorphic forms of weight one I, Nagoya Math. J., 85 (1982), 213–221.CrossRefGoogle Scholar
[2] Hiramatsu, T., On some dimension formula for automorphic forms of weight one II, Nagoya Math. J., 105 (1987), 169–186.CrossRefGoogle Scholar
[3] Hiramatsu, T., A formula for the dimension of spaces of cusp forms of weight 1, to appear in Advanced Studies in Pure Math., 15.Google Scholar
[4] Kubota, T., Elementary theory of Eisenstein series, Tokyo-New York: Kodansha and Halsted 1973.Google Scholar
[5] Selberg, A, Discontinuous groups and harmonic analysis, in Proc. Int. Math. Congr., Stockholm, 177–189, 1962.Google Scholar