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 $\mathcal{U}$ and $\mathcal{V}$ of which the additive energy of $\mathcal{U}$ and $f(\mathcal{V})$ 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.
Citation
Simon Macourt. "Decomposition of subsets of finite fields." Funct. Approx. Comment. Math. 61 (2) 243 - 255, December 2019. https://doi.org/10.7169/facm/1752