Work

Poisson Approximation of Prime Divisors of Shifted Primes

Year: 2025

Type: article

Abstract: We develop an analog for shifted primes of the Kubilius model of prime factors of integers. We prove a total variation distance estimate for the difference between the model and actual prime factors of shifted primes, and apply it to show that the prime factors of shifted primes in disjoint sets behave like independent Poisson variables. As a consequence, we establish a transference principle between the anatomy of random integers $\leqslant x$ and of random shifted primes $p+a$ with $p\leqslant x$.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnaf079

Author: Kevin Ford

Institution: University of Illinois Urbana-Champaign

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Sieves and primes, Primes, Divisors, and Permutations