Vol. 2, No. 2, 2009

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Roth's theorem in $\mathbb{Z}_4^n$

Tom Sanders

Vol. 2 (2009), No. 2, 211–234
Abstract

We show that if A 4n contains no three-term arithmetic progressions in which all the elements are distinct then |A| = o(4nn).

Keywords
Roth–Meshulam, cap set problem, Fourier, Freĭman, Balog–Szemerédi, characteristic 2, $\mathbb Z_4^n$, three-term arithmetic progressions
Mathematical Subject Classification 2000
Primary: 42A05
Milestones
Received: 14 November 2008
Revised: 30 March 2009
Accepted: 4 May 2009
Published: 1 May 2009
Authors
Tom Sanders
Department of Pure Mathematics and Mathematical Statistics
University of Cambridge
Cambridge, CB3 0WA
United Kingdom
http://www.dpmms.cam.ac.uk/~tws22/