An uncertainty principle for arithmetic sequences

• 成果类型: Article
• 署名作者: Granville, Andrew; Soundararajan, K.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2007.165.593
• 发表日期: 2007
• 页码: 593-635
• 关键词: sums

摘要

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.