An uncertainty principle for arithmetic sequences


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.


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