Type: Article

Sumsets of reciprocal in prime fields and multilinear Kloosterman sums

Bourgain, Zh; Garaev, M. Z;

Abstract:

We obtain new results on the additive properties of the set I-1 = {x(-1) : x is an element of I}, where I is an arbitrary interval in the field of residue classes modulo a large prime p. Combining our results with estimates of multilinear exponential sums, we obtain new results on incomplete multilinear Kloosterman sums.