Bounded gaps between primes in short intervals

被引：3
作者：
Alweiss R. [1 ]
Luo S. [1 ]
机构：
[1] Massachusetts Institute of Technology, Cambridge, MA
来源：
Research in Number Theory | 2018年 / 4卷 / 2期
基金：
美国国家科学基金会;
关键词：
Bounded gaps; Short intervals;
D O I：
10.1007/s40993-018-0109-y
中图分类号：
学科分类号：
摘要：
Baker, Harman, and Pintz showed that a weak form of the Prime Number Theorem holds in intervals of the form [ x- x0.525, x] for large x. In this paper, we extend a result of Maynard and Tao concerning small gaps between primes to intervals of this length. More precisely, we prove that for any δ∈ [ 0.525 , 1 ] there exist positive integers k, d such that for sufficiently large x, the interval [ x- xδ, x] contains ≫kxδ(logx)k pairs of consecutive primes differing by at most d. This confirms a speculation of Maynard that results on small gaps between primes can be refined to the setting of short intervals of this length. © 2018, SpringerNature.
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