Distribution of residues in approximate subgroups of 𝔽_{𝕡}*

Hegyvári, Norbert; Hennecart, François

doi:10.1090/S0002-9939-2011-10866-9

Distribution of residues in approximate subgroups of $\mathbb {F}_p^*$
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Proc. Amer. Math. Soc. 140 (2012), 1-6 Request permission

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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