Diaphony, a measure of uniform distribution, and the Patterson function

This paper reviews the number‐theoretic concept of diaphony, a measure of uniform distribution for number sequences and point sets based on a Fourier theory approach, and its relation to crystallographic concepts like the largest interplanar spacing of a lattice, the structure‐factor equation and th...

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Bibliographic Details
Published in:Acta crystallographica. Section A, Foundations and advances Foundations and advances, 2015-07, Vol.71 (4), p.382-391
Main Authors: Hornfeck, Wolfgang, Kuhn, Philipp
Format: Article
Language:English
Subjects:
Crystallography
diaphony
Foundations
Fourier analysis
geometric discrepancy
Lattice theory
Lattices
Mathematical analysis
Number theory
Patterson function
Sequences
structure‐factor equation
uniform distribution
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Summary:This paper reviews the number‐theoretic concept of diaphony, a measure of uniform distribution for number sequences and point sets based on a Fourier theory approach, and its relation to crystallographic concepts like the largest interplanar spacing of a lattice, the structure‐factor equation and the Patterson function.
ISSN:2053-2733
0108-7673
2053-2733
DOI:10.1107/S2053273315007123