Large prime gaps and progressions with few primes
Number Theory
2022-07-05 v4
Abstract
We show that the existence of arithmetic progressions with few primes, with a quantitative bound on "few", implies the existence of larger gaps between primes less than x than is currently known unconditionally. In particular, we derive this conclusion if there are certain types of exceptional zeros of Dirichlet L-functions.
Cite
@article{arxiv.1907.11994,
title = {Large prime gaps and progressions with few primes},
author = {Kevin Ford},
journal= {arXiv preprint arXiv:1907.11994},
year = {2022}
}
Comments
re-organized the description of the corollaries; typos corrected