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Estimates for trilinear and quadrilinear character sums

  • Étienne Fouvry

    Université Paris-Saclay, Orsay Cedex, France

  • Igor E. Shparlinski

    University of New South Wales, Sydney, Australia

  • Ping Xi

    Xi’an Jiaotong University, Xi’an, P. R. China
Estimates for trilinear and quadrilinear character sums cover
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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 Sárközy (1987) and the solvability of some prime type equations with constraints.

Cite this article

Étienne Fouvry, Igor E. Shparlinski, Ping Xi, Estimates for trilinear and quadrilinear character sums. Rev. Mat. Iberoam. (2025), published online first

DOI 10.4171/RMI/1530