Fourier Analysis and Szemer Edi's Theorem

@inproceedings{Gowers1998FourierAA,
  title={Fourier Analysis and Szemer Edi's Theorem},
  author={W. T. Gowers},
  year={1998}
}
The famous theorem of Szemer edi asserts that for every positive integer k and every positive real number > 0 there is a positive integer N such that every subset of f1; 2; : : :; Ng of cardinality at least N contains an arithmetic progression of length k. A second proof of the theorem was given by Furstenberg using ergodic theory, but neither this proof nor Szemer edi's gave anything other than extremely weak information about the dependence of N on k and. In this article we describe a new… CONTINUE READING
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References

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On certain sets of integers

K. F. Roth
J. London Math. Soc • 1953

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