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Distribution of residues in approximate subgroups of $\mathbb {F}_p^*$

Authors: Norbert Hegyvári and François Hennecart
Journal: Proc. Amer. Math. Soc. 140 (2012), 1-6
MSC (2010): Primary 11B75
Published electronically: May 3, 2011
MathSciNet review: 2833512
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Abstract: We extend a result due to Bourgain on the uniform distribution of residues by proving that subsets of the type $f(I)\cdot H$ are equidistributed (as $p$ tends to infinity), where $f$ is a polynomial, $I$ is an interval of $\mathbb {F}_p$ and $H$ is an approximate subgroup of $\mathbb {F}_p^*$ with size larger than polylogarithmic in $p$.

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Additional Information

Norbert Hegyvári
Affiliation: Institute of Mathematics, Eötvös University, H-1117 Pázmány st. 1/c, Budapest, Hungary

François Hennecart
Affiliation: Université de Lyon and Université Jean-Monnet, 23, rue Michelon, 42023 Saint-Étienne, France

Received by editor(s): June 7, 2010
Received by editor(s) in revised form: October 26, 2010
Published electronically: May 3, 2011
Additional Notes: Research of the first author is partially supported by OTKA grants K 61908 and K 67676. He is grateful to the members of the LAMUSE (Laboratory of Mathematics of the University of Saint-Etienne) for their warm hospitality during his stay
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2011 American Mathematical Society