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Fourier-Eisenstein transform and plancherel formula for rational binary quadratic forms

Published online by Cambridge University Press:  22 January 2016

Yumiko Hironaka  and
Fumihiro Sato
Yumiko Hironaka
Affiliation:
Department of Mathematics, Faculty of Science, Shinshu University, Matsumoto 390, Japan
Fumihiro Sato
Affiliation:
Department of Mathematics, Rikkyo University, Nishi-Ikebukuro, Toshimaku, Tokyo 171, Japan
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Let X be the space of nondegenerate rational symmetric matrices of size 2 and put

The group G acts on X by

We are interested in the space (Γ\X) of Γ-invariant C-valued functions on X and its subspace &(Γ\X) of functions whose supports consist of a finite number of Γ-orbits. The Hecke algebra ℋ(G, Γ) of G with respect to Γ acts naturally on these spaces.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 128 , December 1992 , pp. 121 - 151
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1992

References

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