Abstract
We obtain a series of estimates on the number of small integers and small order Farey fractions that 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 k1 and x k2 modulo p and to a question of Holden and Moree on fixed points of the discrete logarithm.
Original language | English |
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Pages (from-to) | 1968-2009 |
Number of pages | 42 |
Journal | International Mathematics Research Notices |
Volume | 2012 |
Issue number | 9 |
DOIs | |
Publication status | Published - 2012 |