Distribution of Elements of Cosets of Small Subgroups and Applications

Details Distribution of Elements of Cosets of Small Subgroups and Applications Distribution of Elements of Cosets of Small Subgroups and Applications

2011-03-01

arxiv.org/abs/1103.0296v2

Mathematics

Number Theory

Duplicated submission, see also http://arxiv.org/abs/1103.0567

Scientific paper

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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