Matteo Bordignon: Weyl sums with multiplicative coefficients and joint equidistribution

Abstract:

 In this talk I will present a joint work with Cynthia Bortolotto and Bryce Kerr, where we generalize a result of Montgomery and Vaughan regarding exponential sums with multiplicative coefficients 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.