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arXiv · 0802.4371

On additive doubling and energy

Nets Hawk Katz·Paul Koester
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Abstract

We show that if A is a set having small subtractive doubling in an abelian group, that is |A-A|< K|A|, then there is a polynomially large subset B of A-A so that the additive energy of B is large than (1/K)^{1 - ε) where epsilon is a positive, universal exponent. (1/37 seems to suffice.)

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Nets Hawk Katz, Paul Koester. 2008-02-29. On additive doubling and energy. https://arxiv.org/abs/0802.4371

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