Mobius cancellation on polynomial sequences and the quadratic Bateman-Horn conjecture over function fields

• 成果类型: Article
• 署名作者: Sawin, Will; Shusterman, Mark
• 署名单位: Columbia University; Harvard University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01115-y
• 发表日期: 2022
• 页码: 751-927
• 关键词: sums

摘要

We establish cancellation in short sums of certain special trace functions over F-q [u] belowthe Polya-Vinogradov range, with savings approaching square-root cancellation as q grows. This is used to resolve the F-q [u]-analog of Chowla's conjecture on cancellation in Mobius sums over polynomial sequences, and of the Bateman-Horn conjecture in degree 2, for some values of q. A final application is to sums of trace functions over primes in F-q [u].