A Weighted Divisor Problem

Lirui Jia; Wenguang Zhai

A Weighted Divisor Problem

Number Theory 2016-11-24 v3

Authors: Lirui Jia , Wenguang Zhai

Abstract

We study a weighted divisor function $\mathop{{\sum}'}\limits_{mn\leq x}\cos(2\pi m\theta_1)\sin(2\pi n\theta_2)$ , where $\theta_i (0<\theta_i<1)$ is a rational number. By connecting it with the divisor problem with congruence conditions, we establish the upper bound, mean-value, mean-square and some power-moments.

Keywords

multiplicative functions divisor function weighted inequalities

Cite

@article{arxiv.1602.06160,
  title  = {A Weighted Divisor Problem},
  author = {Lirui Jia and Wenguang Zhai},
  journal= {arXiv preprint arXiv:1602.06160},
  year   = {2016}
}

Related papers

View all related →