Algebraic twists of modular forms and Hecke orbits
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Date
2015-04
Publication Type
Journal Article
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yes
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Abstract
We consider the question of the correlation of Fourier coefficients of modular forms with functions of algebraic origin. We establish the absence of correlation in considerable generality (with a power saving of Burgess type) and a corresponding equidistribution property for twisted Hecke orbits. This is done by exploiting the amplification method and the Riemann Hypothesis over finite fields, relying in particular on the ℓ-adic Fourier transform introduced by Deligne and studied by Katz and Laumon.
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published
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Volume
25 (2)
Pages / Article No.
580 - 657
Publisher
Springer
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Subject
Modular forms; Fourier coefficients; Hecke eigenvalues; Hecke orbits; Horocycles; l-adic Fourier transform; Riemann Hypothesis over finite fields
Organisational unit
03796 - Kowalski, Emmanuel / Kowalski, Emmanuel
Notes
Dedicated to Peter Sarnak on his 61st birthday, with admiration.