The irrationality of a prime factor series under a prime tuples conjecture
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929511144095744 |
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| author | Pratt, Kyle |
| author_facet | Pratt, Kyle |
| contents | Let $ω(n)$ denote the number of distinct prime factors of $n$. Assuming a suitably uniform version of the prime $k$-tuples conjecture, we show that the number \begin{align*} \sum_{n=1}^\infty \frac{ω(n)}{2^n} \end{align*} is irrational. This settles (conditionally) a question of Erdős. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15185 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The irrationality of a prime factor series under a prime tuples conjecture Pratt, Kyle Number Theory Let $ω(n)$ denote the number of distinct prime factors of $n$. Assuming a suitably uniform version of the prime $k$-tuples conjecture, we show that the number \begin{align*} \sum_{n=1}^\infty \frac{ω(n)}{2^n} \end{align*} is irrational. This settles (conditionally) a question of Erdős. |
| title | The irrationality of a prime factor series under a prime tuples conjecture |
| topic | Number Theory |
| url | https://arxiv.org/abs/2409.15185 |