Flat Littlewood polynomials exist

• 成果类型: Article
• 署名作者: Balister, Paul; Bollobas, Bela; Morris, Robert; Sahasrabudhe, Julian; Tiba, Marius
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2020.192.3.6
• 发表日期: 2020
• 页码: 977-1004
• 关键词: minimum modulus; shapiro; discrepancy

摘要

We show that there exist absolute constants Delta > delta > 0 such that, for all n >= 2, there exists a polynomial P of degree n, with coefficients in { -1, 1}, such that delta root n <= vertical bar P(z)vertical bar <= Delta root n for all z is an element of C with vertical bar z vertical bar = 1. This confirms a conjecture of Littlewood from 1966.