Type: Article

On some congruences and exponential sums

Garaev, Moubariz Z.; Shparlinski, Igor E.;

Abstract:

Let be a fixed small constant, be the finite field of p elements for prime p. We consider additive and multiplicative problems in that involve intervals and arbitrary sets. Representative examples of our results are as follows. Let be an arbitrary subset of . If and or if and then all, but elements of can be represented in the form hm with and , where depends only on ?. Furthermore, let be an arbitrary interval of length H and s be a fixed positive integer. If then the number of solutions to the congruence satisfies