Bounded gaps between primes in short intervals
Abstract Baker, Harman, and Pintz showed that a weak form of the Prime Number Theorem holds in intervals of the form $$[x-x^{0.525},x]$$ [ x - x 0.525 , 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 precis...
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| Format: | Article |
| Language: | English |
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Springer International Publishing,
2021-09-20T17:17:14Z.
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| Online Access: | Get fulltext |
| LEADER | 01168 am a22001453u 4500 | ||
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| 001 | 131478 | ||
| 042 | |a dc | ||
| 100 | 1 | 0 | |a Alweiss, Ryan |e author |
| 700 | 1 | 0 | |a Luo, Sammy |e author |
| 245 | 0 | 0 | |a Bounded gaps between primes in short intervals |
| 260 | |b Springer International Publishing, |c 2021-09-20T17:17:14Z. | ||
| 856 | |z Get fulltext |u https://hdl.handle.net/1721.1/131478 | ||
| 520 | |a Abstract Baker, Harman, and Pintz showed that a weak form of the Prime Number Theorem holds in intervals of the form $$[x-x^{0.525},x]$$ [ x - x 0.525 , 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 $$\delta \in [0.525,1]$$ δ ∈ [ 0.525 , 1 ] there exist positive integers k, d such that for sufficiently large x, the interval $$[x-x^\delta ,x]$$ [ x - x δ , x ] contains $$\gg _{k} \frac{x^\delta }{(\log x)^k}$$ ≫ k x δ ( log x ) 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. | ||
| 546 | |a en | ||
| 655 | 7 | |a Article | |