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

James Maynard

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arXiv · 2006.07088

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

James Maynard

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Abstract

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

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James Maynard. 2020-06-12. Primes in arithmetic progressions to large moduli II: Well-factorable estimates. https://arxiv.org/abs/2006.07088

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