Bubbles of congruent primes
Number Theory
2019-02-20 v1
Abstract
Shiu proved that if a and q are arbitrary coprime integers, then there exist arbitrarily long strings of consecutive primes which are all congruent to a modulo q. We generalize Shiu's theorem to imaginary quadratic fields, where we prove the existence of "bubbles" containing arbitrarily many primes which are all, up to units, congruent to a modulo q.
Cite
@article{arxiv.1201.5400,
title = {Bubbles of congruent primes},
author = {Frank Thorne},
journal= {arXiv preprint arXiv:1201.5400},
year = {2019}
}
Comments
16 pages. A somewhat old paper, recently revised