A Generalization of Roth's Theorem in Function Fields
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Date
2012-11
Authors
Liu, Yu-Ru
Zhao, Xiaomei
Journal Title
Journal ISSN
Volume Title
Publisher
University of Michigan, Department of Mathematics
Abstract
For n ∈ N = {1, 2, ...}, let D3([1, n]) denote the maximal cardinality of an integer
subset of [1, n] containing no nontrivial 3-term arithmetic progression. In a fundamental paper [9], Roth proved that D3([1, n]) n/log log n. His result was later
improved by Heath-Brown [4] and Szemerédi [11] to D3([1, n]) n/(log n)α for
some small positive constant α > 0 (α = 1/20 in [11]). By introducing the notion of Bohr sets, Bourgain [2; 3] further improved this bound and showed that
D3([1, n]) n(log log n)2
/(log n)2/3
Description
Copyright © 2012 The University of Michigan