On the asymptotic densities of certain subsets of $\bf N^k$
| dc.creator | Tóth, László | |
| dc.date | 2006-10-19 | |
| dc.date.accessioned | 2026-07-07T07:29:13Z | |
| dc.date.available | 2026-07-07T07:29:13Z | |
| dc.description | We determine the asymptotic density $δ_k$ of the set of ordered $k$-tuples $(n_1,...,n_k)\in \N^k, k\ge 2$, such that there exists no prime power $p^a$, $a\ge 1$, appearing in the canonical factorization of each $n_i$, $1\le i\le k$, and deduce asymptotic formulae with error terms regarding this problem and analogous ones. We give numerical approximations of the constants $δ_k$ and improve the error term of formula (1.2) due to {\sc E. Cohen}. We point out that our treatment, based on certain inversion functions, is applicable also in case $k=1$ in order to establish asymptotic formulae with error terms regarding the densities of subsets of $\N$ with additional multiplicative properties. These generalize an often cited result of {\sc G. J. Rieger}. | |
| dc.identifier | https://arxiv.org/abs/math/0610582 | |
| dc.identifier | http://arxiv.org/abs/math/0610582 | |
| dc.identifier | Riv. Mat. Univ. Parma (6) 4 (2001), 121-131 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/118019 | |
| dc.subject | Number Theory | |
| dc.subject | 11A25, 11N37 | |
| dc.title | On the asymptotic densities of certain subsets of $\bf N^k$ | |
| dc.type | text |