## Bounded gaps between primes in number fields and function fields

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- by Abel Castillo, Chris Hall, Robert J. Lemke Oliver, Paul Pollack and Lola Thompson PDF
- Proc. Amer. Math. Soc.
**143**(2015), 2841-2856 Request permission

## 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 $\mathbb {F}_q(t)$.## References

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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
- MR Author ID: 47581
- Email: chall14@uwyo.edu
**Robert J. Lemke Oliver**- Affiliation: Department of Mathematics, Stanford University, Palo Alto, California 94305
- MR Author ID: 894148
- Email: rjlo@stanford.edu
**Paul Pollack**- Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
- MR Author ID: 830585
- Email: pollack@uga.edu
**Lola Thompson**- Affiliation: Department of Mathematics, Oberlin College, Oberlin, Ohio 44074
- MR Author ID: 970890
- Email: lola.thompson@oberlin.edu
- 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
- © Copyright 2015 American Mathematical Society
- 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
- MathSciNet review: 3336609