Vol. 8, No. 2, 2019
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A family of four-variable expanders with quadratic growth

Mehdi Makhul
Vol. 8 (2019), No. 2, 143–149
DOI: 10.2140/moscow.2019.8.143
Abstract

We prove that if g(x,y) is a polynomial of degree d that is not a polynomial of only y, then for any finite set A ⊂ ℝ

|X|≫d|A|2, where X :={g(a1,b1) − g(a2,b2) b2 − b1 : a1,a2,b1,b2 ∈ A}.

We will see this bound is also tight for some polynomial g(x,y).

Keywords
Bisector, expander functions
Mathematical Subject Classification 2010
Primary: 11B30
Secondary: 11B75
Milestones
Received: 11 May 2018
Revised: 17 July 2018
Accepted: 31 July 2018
Published: 20 May 2019
Authors
Mehdi Makhul
Johann Radon Institute for Computational and Applied Mathematics (RICAM)
Austrian Academy of Sciences, Linz and Research Institute for Symbolic Computation (RISC)
Johannes Kepler University
Linz
Austria