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A NOTE ON FOURIER COEFFICIENTS OF POINCARÉ SERIES

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  21 December 2010

Emmanuel Kowalski ,
Abhishek Saha  and
Jacob Tsimerman
Emmanuel Kowalski
Affiliation:
ETH Zürich – D-MATH, Rämistrasse 101, 8092 Zürich, Switzerland (email: kowalski@math.ethz.ch)
Abhishek Saha
Affiliation:
ETH Zürich – D-MATH, Rämistrasse 101, 8092 Zürich, Switzerland (email: abhishek.saha@math.ethz.ch)
Jacob Tsimerman
Affiliation:
Princeton University, Fine Hall, Princeton NJ 08540, U.S.A. (email: jtsimerm@math.princeton.edu)
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Abstract

We give a short and “soft” proof of the asymptotic orthogonality of Fourier coefficients of Poincaré series for classical modular forms as well as for Siegel cusp forms, in a qualitative form.

MSC classification

Secondary: 11F30: Fourier coefficients of automorphic forms 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
Type
Research Article
Information
Mathematika , Volume 57 , Issue 1 , January 2011 , pp. 31 - 40
Copyright
Copyright © University College London 2011

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References

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