Arithmetic progressions of primes in short intervals

Abstract

Green and Tao proved that the primes contains arbitrarily long arithmetic progressions. We show that, essentially the same proof leads to the following result: The primes in an short interval contains many arithmetic progressions of any given length.

References in corpus (2)

• Higher correlations of divisor sums related to primes III: k-correlations
• A quantitative ergodic theory proof of Szemerédi's theorem