A remark on the distribution of $\sqrt{p}$ modulo one involving primes of special type II
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912641252851712 |
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| author | Li, Runbo |
| author_facet | Li, Runbo |
| contents | Let $P_{r}$ denote an integer with at most $r$ prime factors counted with multiplicity. In this paper we prove that for some $λ< \frac{1}{12}$, the inequality $\{\sqrt{p}\}<p^{-λ}$ has infinitely many solutions in primes $p$ such that $p+2=P_r$, where $r= 4, 5, 6, 7$. Specially, when $r = 4$ we obtain $λ= \frac{1}{15.1}$, which improves Cai's $\frac{1}{15.5}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01351 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A remark on the distribution of $\sqrt{p}$ modulo one involving primes of special type II Li, Runbo Number Theory Let $P_{r}$ denote an integer with at most $r$ prime factors counted with multiplicity. In this paper we prove that for some $λ< \frac{1}{12}$, the inequality $\{\sqrt{p}\}<p^{-λ}$ has infinitely many solutions in primes $p$ such that $p+2=P_r$, where $r= 4, 5, 6, 7$. Specially, when $r = 4$ we obtain $λ= \frac{1}{15.1}$, which improves Cai's $\frac{1}{15.5}$. |
| title | A remark on the distribution of $\sqrt{p}$ modulo one involving primes of special type II |
| topic | Number Theory |
| url | https://arxiv.org/abs/2401.01351 |