Bounded gaps between primes in number fields and function fields

Abel Castillo, Chris Hall, Robert J. Lemke Oliver, Paul Pollack, Lola Thompson

Published 2014-03-23Version 1

The Hardy--Littlewood prime $k$-tuples conjecture has long been thought to be completely unapproachable with current methods. While this sadly remains true, startling breakthroughs of Zhang, Maynard, and Tao have nevertheless made significant progress toward this problem. In this work, we extend the Maynard-Tao method to both number fields and the function field $\mathbb{F}_q(t)$.