Bounded gaps between primes in number fields and function fields

2014/03/23 by Abel Castillo, Castillo, Abel, Chris Hall +7 · 1 citation
Mathematics · #Analytic Number Theory Research #Algebraic Geometry and Number Theory #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1403.5808

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 \mathbbF_q(t).

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• Prime-free discs in imaginary quadratic fields
• The existence of small prime gaps in subsets of the integers

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