Sumsets of reciprocals in prime fields and multilinear Kloosterman sums

Abstract: We obtain new results on additive properties of the set $$ I^{-1}= {x^{-1}: \quad x\in I} $$ where $I$ is an arbitrary interval in the field of residue classes modulo a large prime $p$. We combine our results with multilinear exponential sum estimates and obtain new results on incomplete multilinear Kloosterman sums.