One-Dimensional Crystals and Quadratic Residues

  title={One-Dimensional Crystals and Quadratic Residues},
  author={Fernando Chamizo and Antonio Manj{\'o}n-Cabeza C{\'o}rdoba},
  journal={Journal of Number Theory},
Abstract The main problem in crystallography is recovering the electronic density from the diffraction peak intensities. The one-dimensional model leads to recover a discrete Fourier series in Z nwith integral coefficients from its absolute value, which has arithmetical implications. In this paper we prove that the constant absolute value of Gaussian sums determines them among a class of exponential sums. This implies that if diffraction peak intensities are constant except for one of them… 



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