# 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 $p$.
Type de document :
Article dans une revue
Proceedings of the American Mathematical Society, American Mathematical Society, 2012, 140, pp.1-6
Domaine :

https://hal.archives-ouvertes.fr/hal-00867368
Contributeur : François Hennecart <>
Soumis le : dimanche 29 septembre 2013 - 13:35:51
Dernière modification le : mercredi 12 décembre 2018 - 15:31:51

### Identifiants

• 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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