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

2020/08/22 by Will Sawin, Mark Shusterman, Sawin, Will +1
Computer Science · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.2008.09905

arxiv created 2020/08/22 · openalex publication_date 2020/08/22 · arxiv updated 2020/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish cancellation in short sums of certain special trace functions over \mathbbF_q[u] below the Pólya-Vinogradov range, with savings approaching square-root cancellation as q grows. This is used to resolve the \mathbbF_q[u]-analog of Chowla's conjecture on cancellation in Möbius 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 \mathbbF_q[u].

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