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Bubbles of Congruent Primes

Published online by Cambridge University Press:  04 November 2014

FRANK THORNE
FRANK THORNE*
Affiliation:
Department of Mathematics, University of South Carolina, 1523 Greene Street, Columbia, SC 29208U.S.A e-mail: [email protected]
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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 

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References

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