Distribution of elements of cosets of small subgroups and applications

Jean Bourgain*, Sergei V. Konyagin, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


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 languageEnglish
Pages (from-to)1968-2009
Number of pages42
JournalInternational Mathematics Research Notices
Issue number9
Publication statusPublished - 2012


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