Generalized lattice-point visibility in ?k

It is a well-known result that the proportion of lattice points visible from origin given by $\frac{1}{\zeta(2)}$, where $\zeta(s)=\sum_{n=1}^\infty\frac{1}{n^s}$ denotes Riemann zeta function. Goins, Harris, Kubik and Mbirika, generalized notion point visibility saying for fixed $b\in\mathbb{N}$, $(r,s)\in\mathbb{N}^2$ $b$-visible if no other lies on graph function $f(x)=mx^b$, some $m\in\mathbb{Q}$, between $(r,s)$. In their analysis they establish $\frac{1}{\zeta(b+1)}$, which generalizes in classical setting. this short note we give an $n$-dimensional $\bf{b}$-visibility recovers one presented Goins et. al. $2$-dimensions, $n$-dimensions. We prove ${\bf{b}}=(b_1,b_2,\ldots,b_n)\in\mathbb{N}^n$ ${\bf{b}}$-visible $\frac{1}{\zeta(\sum_{i=1}^nb_i)}$. Moreover, propose vectors $\bf{b}\in \mathbb{Q}_{>0}^n$, show imposing weak conditions those obtains density ${\bf{b}}=(\frac{b_1}{a_1},\frac{b_2}{a_2},\ldots,\frac{b_n}{a_n})\in\mathbb{Q}_{>0}^n$-visible Finally, (\mathbb{Q}^{*})^n$, compatible with previous notion, results Harris Omar $b\in \mathbb{Q}^{*}$ $2$-dimensions; $\bf{b}$-visible case only depends negative entries $\bf{b}$.