Estimates for trilinear and quadrilinear character sums
Number Theory
2025-03-20 v4
Abstract
We obtain new bounds on some trilinear and quadrilinear character sums, which are non-trivial starting from very short ranges of the variables. An application to an apparently new problem on oscillations of characters on differences between Farey fractions is given. Other applications include a modular analogue of a multiplicative hybrid problem of Iwaniec and S\'ark\"ozy (1987) and the solvability of some prime type equations with constraints.
Keywords
Cite
@article{arxiv.2404.09295,
title = {Estimates for trilinear and quadrilinear character sums},
author = {Étienne Fouvry and Igor E. Shparlinski and Ping Xi},
journal= {arXiv preprint arXiv:2404.09295},
year = {2025}
}
Comments
32 pages. To appear in Rev. Mat. Iberoam