Asymptotic formula for sum-free sets in abelian groups

Details Asymptotic formula for sum-free sets in abelian groups Asymptotic formula for sum-free sets in abelian groups

2005-07-13

arxiv.org/abs/math/0507259v1

Mathematics

Number Theory

9 pages, no figures

Scientific paper

Let A be a subset of a finite abelian group G. We say that A is sum-free if there is no solution of the equation x + y = z, with x, y, z belonging to the set A. Let SF(G) denotes the set of all sum-free subets of $G$ and $\sigma(G)$ denotes the number $ n^{-1}(\log_2 |SF(G)|) $. In this article we shall improve the error term in the asymptotic formula of $\sigma(G)$ which was obtained recently by Ben Green and Ruzsa. The methods used are a slight refinement of methods developed by Ben Green and Ruzsa.

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