Primes in arithmetic progressions to large moduli II: Well-factorable estimates

2020/06/12 by James Maynard, Maynard, James · 4 citations
Mathematics · #11N05 #11N35 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2006.07088

openalex publication_date 2020/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish new mean value theorems for primes of size x in arithmetic progressions to moduli as large as x^3/5-ε when summed with suitably well-factorable weights. This extends well-known work of Bombieri, Friedlander and Iwaniec, who handled moduli of size at most x^4/7-ε. This has consequences for the level of distribution for sieve weights coming from the linear sieve.

Citations

• Primes in arithmetic progressions to large moduli
• Prime Numbers in Short Intervals and a Generalized Vaughan Identity
• Binary Goldbach under EH(θ) and a Thin-Set BDH Mean-Square via a Hybrid Minor-Arc Method

Cited by

• Primes in simultaneous arithmetic progressions
• Bilinear forms with Kloosterman sums via quadratic characters
• A modification of the linear sieve, and the count of twin primes
• Small gaps between Goldbach primes

Related

• Binary Goldbach under EH(θ) and a Thin-Set BDH Mean-Square via a Hybrid Minor-Arc Method
• Primes in arithmetic progressions to large moduli III: Uniform residue classes
• A modification of the linear sieve, and the count of twin primes
• Primes in arithmetic progressions to large moduli, and shifted primes without large prime factors
• Primes in arithmetic progressions to large moduli, and Goldbach beyond the square-root barrier