Multiplicative congruences with variables from short intervals

Jean Bourgain*, Moubariz Z. Garaev, Sergei V. Konyagin, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


Recently, several bounds have been obtained on the number of solutions of congruences of the type (formula presented) where p is prime and variables take values in some short interval. Here, for almost all p and all s and also for a fixed p and almost all s, we derive stronger bounds. We also use similar ideas to show that for almost all p, one can always find an element of a large order in any rather short interval.

Original languageEnglish
Pages (from-to)117-147
Number of pages31
JournalJournal d'Analyse Mathematique
Issue number1
Publication statusPublished - Oct 2014
Externally publishedYes


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