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arXiv · 2011.13891

Additive double character sums over some structured sets and applications

Cathy Swaenepoel·Arne Winterhof
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Abstract

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 S\'ark\"ozy.

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Cathy Swaenepoel, Arne Winterhof. 2020-11-27. Additive double character sums over some structured sets and applications. https://arxiv.org/abs/2011.13891

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