Correlation of arithmetic functions over Fq[T]

Ofir Gorodetsky, Will Sawin

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


For a fixed polynomial Δ, we study the number of polynomials f of degree n over Fq such that f and f+ Δ are both irreducible, an Fq[T] -analogue of the twin primes problem. In the large-q limit, we obtain a lower-order term for this count if we consider non-monic polynomials, which depends on Δ in a manner which is consistent with the Hardy–Littlewood Conjecture. We obtain a saving of q if we consider monic polynomials only and Δ is a scalar. To do this, we use symmetries of the problem to get for free a small amount of averaging in Δ. This allows us to obtain additional saving from equidistribution results for L-functions. We do all this in a combinatorial framework that applies to more general arithmetic functions than the indicator function of irreducibles, including the Möbius function and divisor functions.

Original languageEnglish (US)
Pages (from-to)1059-1106
Number of pages48
JournalMathematische Annalen
Issue number3-4
StatePublished - Apr 1 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics


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