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Bounded gaps between primes in number fields and function fields


Authors: Abel Castillo, Chris Hall, Robert J. Lemke Oliver, Paul Pollack and Lola Thompson
Journal: Proc. Amer. Math. Soc. 143 (2015), 2841-2856
MSC (2010): Primary 11N05, 11N36, 11T06
DOI: https://doi.org/10.1090/S0002-9939-2015-12554-3
Published electronically: February 25, 2015
MathSciNet review: 3336609
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Abstract: 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 $ \mathbb{F}_q(t)$.


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Additional Information

Abel Castillo
Affiliation: Department of Mathematics, University of Illinois at Chicago, Chicago, Illinois 60607
Email: acasti8@uic.edu

Chris Hall
Affiliation: Department of Mathematics, University of Wyoming, Laramie, Wyoming 82071
Email: chall14@uwyo.edu

Robert J. Lemke Oliver
Affiliation: Department of Mathematics, Stanford University, Palo Alto, California 94305
Email: rjlo@stanford.edu

Paul Pollack
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
Email: pollack@uga.edu

Lola Thompson
Affiliation: Department of Mathematics, Oberlin College, Oberlin, Ohio 44074
Email: lola.thompson@oberlin.edu

DOI: https://doi.org/10.1090/S0002-9939-2015-12554-3
Received by editor(s): March 25, 2014
Published electronically: February 25, 2015
Additional Notes: The second author was partially supported by a grant from the Simons Foundation (245619)
The third author was supported by an NSF Mathematical Sciences Postdoctoral Research Fellowship
Communicated by: Ken Ono
Article copyright: © Copyright 2015 American Mathematical Society