English

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