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arXiv · 1003.5347

On the Restricted Divisor Function in Arithmetic Progressions

Igor E. Shparlinski
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Abstract

We obtain several asymptotic estimates for the sums of the restricted divisor function $$ \tau_{M,N}(k) = #\{1 \le m \le M, \ 1\le n \le N: mn = k\} $$ over short arithmetic progressions, which improve some results of J. Truelsen. Such estimates are motivated by the links with the pair correlation problem for fractional parts of the quadratic function $\alpha k^2$, $k=1,2,...$ with a real $\alpha$.

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Igor E. Shparlinski. 2010-03-28. On the Restricted Divisor Function in Arithmetic Progressions. https://arxiv.org/abs/1003.5347

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