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On some dimension formula for automorphic forms of weight one I

Published online by Cambridge University Press:  22 January 2016

Toyokazu Hiramatsu
Toyokazu Hiramatsu*
Affiliation:
Department of Mathematics, Kobe University
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Let Γ be a fuchsian group of the first kind not containing the element . We shall denote by d0 the number of linearly independent automorphic forms of weight 1 for Γ. It would be interesting to have a certain formula for d0 . But, Hejhal said in his Lecture Notes 548, it is impossible to calculate d0 using only the basic algebraic properties of Γ. On the other hand, Serre has given such a formula of d0 recently in a paper delivered at the Durham symposium ([7]). His formula is closely connected with 2-dimensional Galois representations.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 85 , March 1982 , pp. 213 - 221
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

References

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