Multiple Exponential and Character Sums with Monomials

Abstract

We obtain new bounds of multivariate exponential sums with monomials, when the variables run over rather short intervals. Furthermore, we use the same method to derive estimates on similar sums with multiplicative characters to which previously known methods do not apply. In particular, in the multiplicative characters modulo a prime $p$ we break the barrier of $p^{1/4}$ for ranges of individual variables.

References in corpus (3)

• Vinogradov's mean value theorem via efficient congruencing
• Vinogradov's mean value theorem via efficient congruencing, II
• Sumsets of reciprocals in prime fields and multilinear Kloosterman sums