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Structure Along Arithmetic Patterns in Sequences of Vectors

Published online by Cambridge University Press:  30 March 2009

P. CANDELA
P. CANDELA*
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK (e-mail: [email protected])
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Abstract

We discuss a new direction in which the use of some methods from arithmetic combinatorics can be extended. We consider functions taking values in Euclidean space and supported on subsets of {1, 2, . . ., N}. In this context we present a proof of a natural generalization of Szemerédi's theorem. We also prove a similar generalization of a theorem of Sárkőzy using a vector-valued Fourier transform, adapting an argument of Green and obtaining effective bounds.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 18 , Issue 6 , November 2009 , pp. 861 - 870
Copyright
Copyright © Cambridge University Press 2009

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