包含除数函数的等差数列的指数和

IF 1.8 3区 数学 Q1 MATHEMATICS
Rui Zhang, Y. Li, Xiao-Hui Yan
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引用次数: 0

摘要

设$ \phi(x) $为$ [1, 2] $上支持的平滑函数,其导数以$ \phi^{(j)}(x)\ll 1 $和$ d_3(n) $为界,表示将$ n $写成三因子乘积的方法的数目。我们得到了非线性指数和的渐近公式$ \sum\limits_{n\ \equiv\ l\ mod\ q}d_3(n)\phi\left(\frac{n}{X}\right)e\left(\frac{3\sqrt[3]{kn}}{q}\right) $。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Exponential sums involving the divisor function over arithmetic progressions
Let $ \phi(x) $ be a smooth function supported on $ [1, 2] $ with derivatives bounded by $ \phi^{(j)}(x)\ll 1 $ and $ d_3(n) $ be the number of ways to write $ n $ as a product of three factors. We get the asymptotic formula for the nonlinear exponential sum $ \sum\limits_{n\ \equiv\ l\ mod\ q}d_3(n)\phi\left(\frac{n}{X}\right)e\left(\frac{3\sqrt[3]{kn}}{q}\right) $.
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来源期刊
AIMS Mathematics
AIMS Mathematics Mathematics-General Mathematics
CiteScore
3.40
自引率
13.60%
发文量
769
审稿时长
90 days
期刊介绍: AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.
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