Decomposition of subsets in finite fields

Simon Macourt

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arXiv · 1803.10935

Decomposition of subsets in finite fields

Simon Macourt

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Abstract

We extend a bound of Roche-Newton, Shparlinski and Winterhof which says any subset of a finite field can be decomposed into two disjoint subset $\cU$ and $\cV$ of which the additive energy of $\cU$ and $f(\cV)$ are small, for suitably chosen rational functions $f$. We extend the result by proving equivalent results over multiplicative energy and the additive and multiplicative energy hybrids.

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Simon Macourt. 2018-03-29. Decomposition of subsets in finite fields. https://arxiv.org/abs/1803.10935

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