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 language | English (US) |
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Pages (from-to) | 457-506 |
Number of pages | 50 |
Journal | Annals of Mathematics |
Volume | 196 |
Issue number | 2 |
DOIs | |
State | Published - Sep 2022 |
Externally published | Yes |
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