Year: 2010
Type: preprint
Abstract: We obtain several asymptotic estimates for the sums of the restricted divisor function $$ τ_{M,N}(k) = #\{1 \le m \le M, \ 1\le n \le N: mn = k\} $$ 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 $αk^2$, $k=1,2,...$ with a real $α$.
Source: arXiv (Cornell University)
Author: Shparlinski, Igor E.
Institution: Macquarie University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2949542194