A Weighted Divisor Problem

Lirui Jia; Wenguang Zhai

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arXiv · 1602.06160

A Weighted Divisor Problem

Lirui Jia·Wenguang Zhai

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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.

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Lirui Jia, Wenguang Zhai. 2016-02-19. A Weighted Divisor Problem. https://arxiv.org/abs/1602.06160

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