On the distribution of $αp^2+β$ modulo one for primes $p$ such that $p+2$ has no more two prime divisors
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911827853574144 |
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| author | Todorova, T. L. |
| author_facet | Todorova, T. L. |
| contents | A classical problem in analytic number theory is to study the distribution of fractional part $αp^k+β,\,k\ge 1$ modulo 1, where $α$ is irrational and $p$ runs over the set of primes. For $k=2$ we consider the subsequence generated by the primes $p$ such that $p+2$ is an almost-prime (the existence of infinitely many such $p$ is another topical result in prime number theory) and prove that its distribution has a similar property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01045 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the distribution of $αp^2+β$ modulo one for primes $p$ such that $p+2$ has no more two prime divisors Todorova, T. L. Number Theory A classical problem in analytic number theory is to study the distribution of fractional part $αp^k+β,\,k\ge 1$ modulo 1, where $α$ is irrational and $p$ runs over the set of primes. For $k=2$ we consider the subsequence generated by the primes $p$ such that $p+2$ is an almost-prime (the existence of infinitely many such $p$ is another topical result in prime number theory) and prove that its distribution has a similar property. |
| title | On the distribution of $αp^2+β$ modulo one for primes $p$ such that $p+2$ has no more two prime divisors |
| topic | Number Theory |
| url | https://arxiv.org/abs/2404.01045 |