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

Will Sawin, Mark Shusterman

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We establish cancellation in short sums of certain special trace functions over Fq[u] below the Pólya–Vinogradov range, with savings approaching square-root cancellation as q grows. This is used to resolve the Fq[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 Fq[u].

Original languageEnglish (US)
Pages (from-to)751-927
Number of pages177
JournalInventiones Mathematicae
Volume229
Issue number2
DOIs
StatePublished - Aug 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics

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