JournalsrmiVol. 28, No. 1pp. 231–238

On the restricted divisor function in arithmetic progressions

  • Igor E. Shparlinski

    University of New South Wales, Sydney, Australia
On the restricted divisor function in arithmetic progressions cover
Download PDF

Abstract

We obtain several asymptotic estimates for the sums of the restricted divisor function

τM,N(k)=#{1mM, 1nN:mn=k}\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 αk2\alpha k^2, k=1,2,k=1,2,\dots with a real α\alpha.

Cite this article

Igor E. Shparlinski, On the restricted divisor function in arithmetic progressions. Rev. Mat. Iberoam. 28 (2012), no. 1, pp. 231–238

DOI 10.4171/RMI/675