Distribution on elements of cosets of small subgroups and applications

Details Distribution on elements of cosets of small subgroups and applications Distribution on elements of cosets of small subgroups and applications

2011-03-02

arxiv.org/abs/1103.0567v1

Mathematics

Number Theory

35 pages

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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