Algebraic twists of modular forms and Hecke orbits

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 a""-adic Fourier transform introduced by Deligne and studied by Katz and Laumon.


Published in:
Geometric And Functional Analysis, 25, 2, 580-657
Year:
2015
Publisher:
Basel, Springer Verlag
ISSN:
1016-443X
Keywords:
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 Record created 2015-05-29, last modified 2018-03-17

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