Energy bounds for modular roots and their applications
Number Theory
2025-09-17 v1
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{\'e}} sums and to a new equidistribution estimate for the set of modular roots of primes.
Cite
@article{arxiv.2103.09405,
title = {Energy bounds for modular roots and their applications},
author = {Bryce Kerr and Ilya D. Shkredov and Igor E. Shparlinski and Alexandru Zaharescu},
journal= {arXiv preprint arXiv:2103.09405},
year = {2025}
}