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One-Dimensional Crystals and Quadratic Residues

✍ Scribed by Fernando Chamizo; Antonio Córdoba

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
275 KB
Volume
65
Category
Article
ISSN
0022-314X

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✦ Synopsis

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 n with 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, then, modulo translations, we obtain a quadratic residue molecule.

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