On prime-producing sieves and distribution of $αp-β$ mod $1$
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912650483466240 |
|---|---|
| author | Li, Runbo |
| author_facet | Li, Runbo |
| contents | The author proves that there are infinitely many primes $p$ such that $\| αp - β\| < p^{-\frac{28}{87}}$, where $α$ is an irrational number and $β$ is a real number. This sharpens a result of Jia (2000) and provides a new triple $(γ, θ, ν)=(\frac{59}{87}, \frac{28}{87}, \frac{1}{29})$ that can produce special primes in Ford and Maynard's work on prime-producing sieves. Our minimum amount of Type-II information required ($ν= \frac{1}{29}$) is less than any previous work on this topic using only traditional Type-I and Type-II information. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13195 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On prime-producing sieves and distribution of $αp-β$ mod $1$ Li, Runbo Number Theory The author proves that there are infinitely many primes $p$ such that $\| αp - β\| < p^{-\frac{28}{87}}$, where $α$ is an irrational number and $β$ is a real number. This sharpens a result of Jia (2000) and provides a new triple $(γ, θ, ν)=(\frac{59}{87}, \frac{28}{87}, \frac{1}{29})$ that can produce special primes in Ford and Maynard's work on prime-producing sieves. Our minimum amount of Type-II information required ($ν= \frac{1}{29}$) is less than any previous work on this topic using only traditional Type-I and Type-II information. |
| title | On prime-producing sieves and distribution of $αp-β$ mod $1$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2504.13195 |