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arXiv · 1103.0567

Distribution on elements of cosets of small subgroups and applications

Jean Bourgain·Sergei Konyagin·Igor Shparlinski
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Abstract

We obtain a series of estimates on the number of small integers and small order Farey fractions which belong to a given coset of a subgroup of order $t$ of the group of units of the residue ring modulo a prime $p$, in the case when $t$ is small compared to $p$. We give two applications of these results: to the simultaneous distribution of two high degree monomials $x^{k_1}$ and $x^{k_2}$ modulo $p$ and to a question of J.Holden and P.Moree on fixed points of the discrete logarithm.

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Jean Bourgain, Sergei Konyagin, Igor Shparlinski. 2011-03-02. Distribution on elements of cosets of small subgroups and applications. https://arxiv.org/abs/1103.0567

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