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Regular version of the site

Working paper

Intersections of multiplicative subgroups and Heilbronn's exponential sum

Vyugin I. V., Shkredov I. D., Solodkova E. V.
The paper is devoted to some applications of Stepanov method. In the first part of the paper we obtain the estimate of the cardinality of the set, which is obtained as an intersection of additive shifts of some different subgroups of F_p^*. In the second part we prove a new upper bound for Heilbron's exponential sum and obtain a series of applications of our result to distribution of Fermat quotients.