Correlations between primes in short intervals on curves over finite fields

TL;DR

This paper establishes an analogue of the Hardy-Littlewood conjecture for the distribution of prime constellations within short intervals over function fields of smooth projective curves over finite fields.

Contribution

It extends classical prime distribution conjectures to the setting of function fields, providing new insights into prime patterns over finite fields.

Findings

Proves an analogue of the Hardy-Littlewood conjecture in function fields.

Describes the asymptotic distribution of prime constellations in short intervals.

Advances understanding of prime distribution in algebraic geometry contexts.

Abstract

We prove an analogue of the Hardy-Littlewood conjecture on the asymptotic distribution of prime constellations in the setting of short intervals in function fields of smooth projective curves over finite fields.