On the Chowla and twin primes conjectures over Fq[T]

Will Sawin, Mark Shusterman

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Using geometric methods, we improve on the function field version of the Burgess bound and show that, when restricted to certain special subspaces, the Möbius function over Fq[T] can be mimicked by Dirichlet characters. Combining these, we obtain a level of distribution close to 1 for the Möbius function in arithmetic progressions and resolve Chowla's k-point correlation conjecture with large uniformity in the shifts. Using a function field variant of a result by Fouvry-Michel on exponential sums involving the Möbius function, we obtain a level of distribution beyond 1=2 for irreducible polynomials, and establish the twin prime conjecture in a quantitative form.

Original languageEnglish (US)
Pages (from-to)457-506
Number of pages50
JournalAnnals of Mathematics
Volume196
Issue number2
DOIs
StatePublished - Sep 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

Keywords

  • Level of distribution for irreducible polynomials
  • Parity barrier over function fields
  • Short character sums
  • Twin irreducible polynomials

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