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.

References in corpus (2)

• Higher correlations of divisor sums related to primes III: k-correlations
• Beyond pair correlation

Cited by in corpus (10)

• The primes contain arbitrarily long polynomial progressions
• The dichotomy between structure and randomness, arithmetic progressions, and the primes
• Long arithmetic progressions of primes
• The Gaussian primes contain arbitrarily shaped constellations
• What is good mathematics?
• Generalising the Hardy-Littlewood Method for Primes
• Obstructions to uniformity, and arithmetic patterns in the primes
• The prime ideals in every class contain arbitrary large truncated classes
• Restriction theory of the Selberg sieve, with applications
• Small gaps between the set of products of at most two primes