Work

Small‐scale distribution of linear patterns of primes

Year: 2024

Type: article

Abstract: Let be a system of linear forms with finite complexity. In their seminal paper, Green and Tao showed the following prime number theorem for values of the system : where are the corresponding local densities. In this paper, we demonstrate limits to equidistribution of these primes on small scales; we show the analog to Maier's result on primes in short intervals. In particular, we show that for all , there exist such that for sufficiently large, there exist boxes of sidelengths at least such that

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.13001

Authors: Mayank Pandey, Katharine Woo

Institution: Princeton University

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,780

Funder: National Science Foundation