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Additive double character sums over some structured sets and applications

Volume 199 / 2021

Cathy Swaenepoel, Arne Winterhof Acta Arithmetica 199 (2021), 135-143 MSC: 11T23, 11T30. DOI: 10.4064/aa190628-19-1 Published online: 23 March 2021


We study additive double character sums over two subsets of a finite field. We show that if there is a suitable rational self-map of small degree of a set $D$, then this set contains a large subset $U$ for which the standard bound on the absolute value of the character sum over $U$ and any subset $C$ (which satisfies some restrictions on its size $|C|$) can be improved. Examples of such suitable self-maps are inversion and squaring. Then we apply this new bound to trace products and sum-product equations and improve results of the first author and of Gyarmati and Sárközy.


  • Cathy SwaenepoelAix Marseille Université
    CNRS, Centrale Marseille
    Institut de Mathématiques de Marseille
    UMR 7373
    163 Avenue de Luminy, Case 907
    13288 Marseille Cedex 9, France
  • Arne WinterhofJohann Radon Institute for
    Computational and Applied Mathematics
    Austrian Academy of Sciences
    Altenberger Str. 69
    4040 Linz, Austria

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