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An uncertainty principle for arithmetic sequences

Andrew Granville·K. Soundararajan
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Abstract

Analytic number theorists usually seek to show that sequences which appear naturally in arithmetic are ``well-distributed'' in some appropriate sense. In various discrepancy problems, combinatorics researchers have analyzed limitations to equi-distribution, as have Fourier analysts when working with the ``uncertainty principle''. In this article we find that these ideas have a natural setting in the analysis of distributions of sequences in analytic number theory, formulating a general principle, and giving several examples.

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Andrew Granville, K. Soundararajan. 2004-06-01. An uncertainty principle for arithmetic sequences. https://arxiv.org/abs/math/0406018

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