Energy bounds for modular roots and their applications

Abstract

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 {\it Sali{é}} sums and to a new equidistribution estimate for the set of modular roots of primes.

References in corpus (2)

• Energies and structure of additive sets
• On the distribution of modular square roots of primes