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15 August 2008 The spectral decomposition of shifted convolution sums
Valentin Blomer, Gergely Harcos
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Duke Math. J. 144(2): 321-339 (15 August 2008). DOI: 10.1215/00127094-2008-038

Abstract

Let π1, π2 be cuspidal automorphic representations of PGL2(R) of conductor 1 and Hecke eigenvalues λπ1,2(n), and let h>0 be an integer. For any smooth compactly supported weight functions W1,2:R×C and any Y>0, a spectral decomposition of the shifted convolution sum m±n=hλπ1(|m|)λπ2(|n|)|mn|W1(mY)W2(nY) is obtained. As an application, a spectral decomposition of the Dirichlet series m,n1mn=hλπ1(m)λπ2(n)(m+n)s(mnm+n)100 is proved for Rs>1/2 with polynomial growth on vertical lines in the s-aspect and uniformity in the h-aspect

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Valentin Blomer. Gergely Harcos. "The spectral decomposition of shifted convolution sums." Duke Math. J. 144 (2) 321 - 339, 15 August 2008. https://doi.org/10.1215/00127094-2008-038

Information

Published: 15 August 2008
First available in Project Euclid: 14 August 2008

zbMATH: 1246.11108
MathSciNet: MR2437682
Digital Object Identifier: 10.1215/00127094-2008-038

Subjects:
Primary: 11F30, 11F70, 11F72
Secondary: 11F12, 11M41

Rights: Copyright © 2008 Duke University Press

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Vol.144 • No. 2 • 15 August 2008
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