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

Abstract : We extend a result due to Bourgain on the uniform distribution of residues by proving that subsets of the type $f(I)\cdot H$ is equidistributed (as $p$ tends to infinity) where $f$ is a polynomial, $I$ is an interval of $\Fp$ and $H$ is an approximate subgroup of $\mathbb{F}_p^*$ with size larger than polylogarithmic in $p$.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-00867368
Contributor : François Hennecart <>
Submitted on : Sunday, September 29, 2013 - 1:35:51 PM
Last modification on : Wednesday, December 12, 2018 - 3:31:51 PM

### Identifiers

• HAL Id : hal-00867368, version 1
• ARXIV : 1207.2648

### Citation

Norbert Hegyvári, Francois Hennecart. Distribution of residues in approximate subgroups of $\mathbb{F}_p^*$. Proceedings of the American Mathematical Society, American Mathematical Society, 2012, 140, pp.1-6. ⟨hal-00867368⟩

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