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Weil type representations and automorphic forms

Published online by Cambridge University Press:  22 January 2016

Toshiaki Suzuki
Toshiaki Suzuki*
Affiliation:
Nagoya University
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During 1934-1936, W. L. Ferrar investigated the relation between summation formulae and Dirichlet series with functional equations, inspired by Voronoi’s works (1904) on summation formula with respect to the numbers of divisors. In [11] A. Weil showed that the automorphic properties of theta series are expressed by generalized Poisson summation formulae with respect to the so-called Weil representation. On the other hand, T. Kubota, in his study of the reciprocity law in a number field, defined a generalized theta series and a generalized Weil type representation of SL(2, C) and obtained similar results to those of A. Weil (1970-1976, [5], [6], [7]). The methods, used by W. L. Ferrar and T. Kubota, to obtain (generalized Poisson) summation formulae depend similarly on functional equations of Dirichlet series (attached to the generalized theta series).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 77 , February 1980 , pp. 145 - 166
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1980

References

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