On the Restricted Divisor Function in Arithmetic Progressions
Number Theory
2010-08-05 v3
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 , with a real .
Cite
@article{arxiv.1003.5347,
title = {On the Restricted Divisor Function in Arithmetic Progressions},
author = {Igor E. Shparlinski},
journal= {arXiv preprint arXiv:1003.5347},
year = {2010}
}