Weyl sums with multiplicative coefficients and joint equidistribution

Abstract

In this paper we generalize a result of Montgomery and Vaughan regarding exponential sums with multiplicative coefcients to the setting of Weyl sums. As applications, we establish a joint equidistribution result for roots of polynomial congruences and polynomial values and obtain some new results for mixed character sums.

41 pages

References in corpus (4)

• Linear correlations of multiplicative functions
• Higher uniformity of bounded multiplicative functions in short intervals on average
• Sums of algebraic trace functions twisted by arithmetic functions
• Burgess bounds for short mixed character sums