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arXiv · 1207.0617

Algebraic twists of modular forms and Hecke orbits

Étienne Fouvry·Emmanuel Kowalski·Philippe Michel
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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 ell-adic Fourier transform introduced by Deligne and studied by Katz and Laumon.

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Étienne Fouvry, Emmanuel Kowalski, Philippe Michel. 2014-11-16. Algebraic twists of modular forms and Hecke orbits. https://arxiv.org/abs/1207.0617

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