Bounded gaps between primes in number fields and function fields

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 Ma...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2015-07, Vol.143 (7), p.2841-2856
Main Authors: CASTILLO, ABEL, HALL, CHRIS, OLIVER, ROBERT J. LEMKE, POLLACK, PAUL, THOMPSON, LOLA
Format: Article
Language:English
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Summary: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 Fq(t).
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-2015-12554-3