Some Constructions In The Inverse Spectral Theory Of Cyclic Groups

  • Ben Green
  • Published 2003 in Combinatorics, Probability & Computing

Abstract

The results of this paper concern the “large spectra” of sets, by which we mean the set of points in Fp at which the Fourier transform of a characteristic function χA, A ⊆ Fp, can be large. We show that a recent result of Chang concerning the structure of the large spectrum is best possible. Chang’s result has already found a number of applications in combinatorial number theory. We also show that if |A| = bp/2c, and if R is the set of points r for which |χ̂A(r)| ≥ αp, then almost nothing can be said about R other than that |R| α−2, a trivial consequence of Parseval’s theorem.

DOI: 10.1017/S0963548302005436

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Cite this paper

@article{Green2003SomeCI, title={Some Constructions In The Inverse Spectral Theory Of Cyclic Groups}, author={Ben Green}, journal={Combinatorics, Probability & Computing}, year={2003}, volume={12}, pages={127-138} }