Exponential sums, twisted multiplicativity and moments

Emmanuel Kowalski, Kannan Soundararajan

Published 2021-07-14Version 1

We study averages over squarefree moduli of the size of exponential sums with polynomial phases. We prove upper bounds on various moments of such sums, and obtain evidence of un-correlation of exponential sums associated to different suitably unrelated and generic polynomials. The proofs combine analytic arguments with the algebraic interpretation of exponential sums and their monodromy groups.