Primes in arithmetic progressions to large moduli III: Uniform residue classes

2020/06/15 by James Maynard, Maynard, James · 2 citations
Mathematics · #11N05 #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2006.08250

openalex publication_date 2020/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove new mean value theorems for primes in arithmetic progressions to moduli larger than x^1/2, extending the Bombieri-Vinogradov theorem to moduli of size x^1/2+δ which have conveniently sized divisors. The main feature of these estimates is that they are completely uniform with respect to the residue classes considered, unlike previous works on primes in arithmetic progressions to large moduli.

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• Primes in simultaneous arithmetic progressions
• Bilinear forms with Kloosterman sums via quadratic characters

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