27 citations · 112 across the 25 of their papers we have counts for
6 papers · 1 filter
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})^{…
A lower bound on the LCM of polynomial sequences
James Maynard, Zeev Rudnick
Let be a polynomial of degree with integer coefficients which is irreducible over the rationals. Cilleruelo conjectured that the least common multiple of the value…
On the Duffin-Schaeffer conjecture
Dimitris Koukoulopoulos, James Maynard
Let be an arbitrary function from the positive integers to the non-negative reals. Consider the set of real numbers for which t…