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Quasirandom Arithmetic Permutations

Joshua N. Cooper
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Abstract

Previously, the author introduced quasirandom permutations, permutations of $\mathbb{Z}_n$ which map intervals to sets with low discrepancy. Here we show that several natural number-theoretic permutations are quasirandom, some very strongly so. Quasirandomness is established via discrete Fourier analysis and the Erdos-Turan inequality, as well as by other means. We apply our results on Sos permutations to make progress on a number of questions relating to the sequence of fractional parts of multiples of an irrational. Several intriguing new open problems are presented throughout the discussion.

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BibTeXRIS

Joshua N. Cooper. 2006-02-28. Quasirandom Arithmetic Permutations. https://arxiv.org/abs/math/0310384

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