B. Kerr

I. Shkredov

I. Shparlinski

A. Zaharescu

Bounds for additive energies of modular roots can be generalised and improved with tools from additive combinatorics and algebraic number theory.

We generalise and improve some recent bounds for additive energies of modular roots. Our arguments use a variety of techniques, including those from additive combinatorics, algebraic number theory and the geometry of numbers. We give applications of these results to new bounds on correlations between Salie sums and to a new equidistribution estimate for the set of modular roots of primes.

Energy bounds for modular roots and their applications