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The spectral decomposition of shifted convolution sums over number fields

  • Péter Maga EMAIL logo
Veröffentlicht/Copyright: 12. Juli 2016

Abstract

Let π1, π2 be cuspidal automorphic representations of GL2 over a number field F with Hecke eigenvalues λπ1(𝔪),λπ2(𝔪). For nonzero integers l1,l2F and compactly supported functions W1,W2 on F×, a spectral decomposition of the shifted convolution sum

l1t1-l2t2=q0t1,t2𝔫λπ1(t1𝔫-1)λπ2(t2𝔫-1)¯𝒩(t1t2𝔫-2)W1(l1t1)W2(l2t2)¯

is obtained for any nonzero fractional ideal 𝔫 and any nonzero element q𝔫.

Award Identifier / Grant number: NK104183

Award Identifier / Grant number: Postdoctoral Grant

Funding statement: The author was partially supported by OTKA grant No. NK104183 and the Postdoctoral Grant of the Hungarian Academy of Sciences.

Acknowledgements

The author is grateful to his advisor, Gergely Harcos, for the guidance during his PhD studies at Central European University, Budapest. The author also thanks Valentin Blomer for all his advices. The research for this paper was a part of the author’s PhD thesis at the Central European University, Budapest, Hungary.

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Received: 2013-12-02
Revised: 2016-04-03
Published Online: 2016-07-12
Published in Print: 2018-11-01

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