arXiv 1511.080702015-11math.NT

Counting $r$-tuples of positive integers with $k$-wise relatively prime components

László Tóth

备注：: 11 pages, revised
发表信息：: Journal of Number Theory 166 (2016), 105-116
DOI：: 10.1016/j.jnt.2016.02.016

英文摘要：

Let $r\ge k\ge 2$ be fixed positive integers. Let $\varrho_{r,k}$ denote the characteristic function of the set of $r$-tuples of positive integers with $k$-wise relatively prime components, that is any $k$ of them are relatively prime. We use the convolution method to establish an asymptotic formula for the sum $\sum_{n_1,\ldots,n_r\le x} \varrho_{r,k}(n_1,\ldots,n_r)$ by elementary arguments. Our result improves the error term obtained by J. Hu (2013).

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