## Abstract

For a fixed polynomial Δ, we study the number of polynomials f of degree n over F_{q} such that f and f+ Δ are both irreducible, an F_{q}[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 language | English (US) |
---|---|

Pages (from-to) | 1059-1106 |

Number of pages | 48 |

Journal | Mathematische Annalen |

Volume | 376 |

Issue number | 3-4 |

DOIs | |

State | Published - Apr 1 2020 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- General Mathematics

## Fingerprint

Dive into the research topics of 'Correlation of arithmetic functions over F_{q}[T]'. Together they form a unique fingerprint.