Small Gaps Between Primes I

Abstract

We use short divisor sums to approximate prime tuples and moments for primes in short intervals. By connecting these results to classical moment problems we are able to prove that a positive proportion of consecutive primes are within a quarter of the average spacing between primes.

Cited by in corpus (2)

• Long arithmetic progressions of primes
• Obstructions to uniformity, and arithmetic patterns in the primes