The irrationality of a divisor function series of Erd\H{o}s and Kac
| Autor: | Pratt, Kyle |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For positive integers $k$ and $n$ let $\sigma_k(n)$ denote the sum of the $k$th powers of the divisors of $n$. Erd\H{o}s and Kac asked whether, for every $k$, the number $\alpha_k = \sum_{n\geq 1} \frac{\sigma_k(n)}{n!}$ is irrational. It is known unconditionally that $\alpha_k$ is irrational if $k\leq 3$. We prove $\alpha_4$ is irrational. Comment: 28 pages |
| Databáze: | arXiv |
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