On the distribution of $αp+β$ modulo one for primes of type $p=ar^2+1$
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916193053442048 |
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| author | Todorova, T. |
| author_facet | Todorova, T. |
| contents | A classical problem in analytic number theory is to study the distribution of fractional part $αp+β$ modulo 1, where $α$ is irrational and $p$ runs over the set of primes. We consider the subsequence generated by the primes $p$ such that $p=ar^2+1$ and prove that its distribution has a similar property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01047 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the distribution of $αp+β$ modulo one for primes of type $p=ar^2+1$ Todorova, T. Number Theory A classical problem in analytic number theory is to study the distribution of fractional part $αp+β$ modulo 1, where $α$ is irrational and $p$ runs over the set of primes. We consider the subsequence generated by the primes $p$ such that $p=ar^2+1$ and prove that its distribution has a similar property. |
| title | On the distribution of $αp+β$ modulo one for primes of type $p=ar^2+1$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2404.01047 |