An uncertainty principle for arithmetic sequences

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 equidistribution, 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.

Authors

Andrew Granville

Département de mathématiques et de statistique
Université de Montréal
CP 6128 succ Centre-Ville
Montréal, QC
Canada

Kannan Soundararajan

Department of Mathematics
Stanford University
Stanford, CA 94305
United States