Structure in sets with logarithmic doubling

Details Structure in sets with logarithmic doubling Structure in sets with logarithmic doubling

2010-02-08

arxiv.org/abs/1002.1552v2

Mathematics

Classical Analysis and ODEs

13 pp. Slightly refined the proof of Theorem 1.3. Replaced finite fields of characteristic 3 with arbitrary finite fields. Upd

Scientific paper

Suppose that G is an abelian group, A is a finite subset of G with |A+A|<
K|A| and eta in (0,1] is a parameter. Our main result is that there is a set L
such that |A cap Span(L)| > K^{-O_eta(1)}|A| and |L| = O(K^eta log |A|). We
include an application of this result to a generalisation of the Roth-Meshulam
theorem due to Liu and Spencer.

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