Average number of squares dividing mn

Andrew V. Lelechenko

Average number of squares dividing mn

Number Theory 2014-12-09 v2

Authors: Andrew V. Lelechenko

Abstract

We study the asymptotic behaviour of $\sum_{m,n\le x} \tau_{1,2}(mn)$ , where $\tau_{1,2}(n) = \sum_{a b^2 = n} 1$ , using multidimensional Perron formula and complex integration method. An asymptotic formula with an error term $O(x^{10/7})$ is obtained.

Keywords

divisor function

Cite

@article{arxiv.1407.1222,
  title  = {Average number of squares dividing mn},
  author = {Andrew V. Lelechenko},
  journal= {arXiv preprint arXiv:1407.1222},
  year   = {2014}
}

Comments

12 pages, 1 figure

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