Sums of singular series with large sets and the tail of the distribution of primes
Sums of singular series with large sets and the tail of the distribution of primes
Abstract In 1976, Gallagher showed that the Hardy–Littlewood conjectures on prime k-tuples imply that the distribution of primes in log-size intervals is Poissonian. He did so by computing average values of the singular series constants over different sets of a fixed size k contained in an interval $[1,h]$ as $h …