STRONGLY -ADDITIVE FUNCTIONS AND DISTRIBUTIONAL PROPERTIES OF THE LARGEST PRIME FACTOR
| Autor: | M. Mkaouar, W. Wannes, M. Amri |
|---|---|
| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Bulletin of the Australian Mathematical Society. 93:177-185 |
| ISSN: | 1755-1633 0004-9727 |
| DOI: | 10.1017/s0004972715001264 |
| Popis: | Let $P(n)$ denote the largest prime factor of an integer $n\geq 2$. In this paper, we study the distribution of the sequence $\{f(P(n)):n\geq 1\}$ over the set of congruence classes modulo an integer $b\geq 2$, where $f$ is a strongly $q$-additive integer-valued function (that is, $f(aq^{j}+b)=f(a)+f(b),$ with $(a,b,j)\in \mathbb{N}^{3}$, $0\leq b). We also show that the sequence $\{{\it\alpha}P(n):n\geq 1,f(P(n))\equiv a\;(\text{mod}~b)\}$ is uniformly distributed modulo 1 if and only if ${\it\alpha}\in \mathbb{R}\!\setminus \!\mathbb{Q}$. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|