Asymptotics of the number of sum-free sets in groups of prime order
From the text: ``Let \(S(G)\) denote the family of all sum-free sets in the group \(G\), and let \(Z_p\) be the group of residues of order \(p\). The number \(s(Z_p)\), where \(p\) is a prime number, was estimated by Lev and Schoen.'' The goal of this paper is to prove the asymptotics of \(s(Z_p)\), where \(Z_p\) is a group of prime order \(p\). Specifically, we show that there are constants \(c_i\) \((i= 1, 2)\) such that, for sufficiently large prime numbers of the form \(p\equiv i\pmod 3\), \[ | S(Z_p)|\sim c_i(p-1)2^{[(p+1)/3]}. \] The proof is based on results of \textit{B. Green} and \textit{I. Z. Ruzsa} [Isr. J. Math. 147, 157--188 (2005; Zbl 1158.11311)]. as well as \textit{J.-M. Deshouillers} and \textit{V. F. Lev} [Bull. Lond. Math. Soc. 40, No. 5, 863--875 (2008; Zbl 1200.11078)]. Some more theorems are proved of related interest.
scientific article; zbMATH DE number 6106391