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Bubbles of Congruent Primes
Published online by Cambridge University Press: 04 November 2014
Abstract
In [15], 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.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 157 , Issue 3 , November 2014 , pp. 443 - 456
- Copyright
- Copyright © Cambridge Philosophical Society 2014