Primes in almost all short intervals
The author sharpens a result of Jia (1996), showing that the interval $[n, n+n^{\frac{1}{21.5}+\varepsilon}]$ contains prime numbers for almost all $n$. Watt's mean value bound, a delicate sieve decomposition and more accurate estimates for integrals are used to good effect.
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| Main Author | |
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| Format | Journal Article |
| Language | English |
| Published |
08.07.2024
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| Subjects | |
| Online Access | Get full text |
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| Summary: | The author sharpens a result of Jia (1996), showing that the interval $[n,
n+n^{\frac{1}{21.5}+\varepsilon}]$ contains prime numbers for almost all $n$.
Watt's mean value bound, a delicate sieve decomposition and more accurate
estimates for integrals are used to good effect. |
|---|---|
| DOI: | 10.48550/arxiv.2407.05651 |