%0 Journal Article
%T Algebraic twists of modular forms and Hecke orbits
%A ¨¦tienne Fouvry
%A Emmanuel Kowalski
%A Philippe Michel
%J Mathematics
%D 2012
%I arXiv
%X 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.
%U http://arxiv.org/abs/1207.0617v5