4 citations · 12 across the 7 of their papers we have counts for
8 papers
Primes in arithmetic progressions to large moduli III: Uniform residue classes
James Maynard
We prove new mean value theorems for primes in arithmetic progressions to moduli larger than , extending the Bombieri-Vinogradov theorem to moduli of size whic…
Primes in arithmetic progressions to large moduli II: Well-factorable estimates
James Maynard
We establish new mean value theorems for primes of size in arithmetic progressions to moduli as large as when summed with suitably well-factorable weights. This ext…
On the Twin Prime Conjecture
James Maynard
We discuss various recent advances on weak forms of the Twin Prime Conjecture.
Gaps between primes
James Maynard
We discuss recent advances on weak forms of the Prime -tuple Conjecture, and its role in proving new estimates for the existence of small gaps between primes and the existence o…
Digits of primes
James Maynard
We survey some different results on the digits of prime numbers, giving a simplified proof of weak forms of a result of Maynard and Mauduit-Rivat.
Sums of two squares in short intervals
James Maynard
We show that there are short intervals containing numbers expressible as the sum of two squares, which is many more than the average when $y=o( (\log{x})^{…