Bilinear sums of Gauss sums
Volume 202 / 2022
Acta Arithmetica 202 (2022), 379-388
MSC: 11L05, 11T23.
DOI: 10.4064/aa210523-3-2
Published online: 7 March 2022
Abstract
We obtain nontrivial upper bounds on bilinear sums of Gauss sums modulo a prime. Our argument is based on a bound of J. Bourgain and M. Z. Garaev (2014) on the additive energy of modular reciprocals and on recent bounds on the additive energy of modular square roots due to A. Dunn, B. Kerr, I. D. Shkredov, I. E. Shparlinski and A. Zaharescu (2020–2021).
