ON SUMS INVOLVING THE EULER TOTIENT FUNCTION

IF 0.6 4区数学 Q3 MATHEMATICS Bulletin of the Australian Mathematical Society Pub Date : 2023-08-24 DOI:10.1017/s0004972723000825

I. Kiuchi, Yuki Tsuruta

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引用次数: 0

Abstract

Let

$\gcd (n_{1},\ldots ,n_{k})$

denote the greatest common divisor of positive integers

$n_{1},\ldots ,n_{k}$

and let

$\phi $

be the Euler totient function. For any real number

$x>3$

and any integer

$k\geq 2$

, we investigate the asymptotic behaviour of

$\sum _{n_{1}\ldots n_{k}\leq x}\phi (\gcd (n_{1},\ldots ,n_{k})). $

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关于涉及欧拉积分函数的和

设$\gcd (n_{1},\ldots ,n_{k})$表示正整数的最大公约数$n_{1},\ldots ,n_{k}$，设$\phi $表示欧拉全数函数。对于任意实数$x>3$和任意整数$k\geq 2$，我们研究了 $\sum _{n_{1}\ldots n_{k}\leq x}\phi (\gcd (n_{1},\ldots ,n_{k})). $

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Bulletin of the Australian Mathematical Society 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

149

审稿时长

4-8 weeks

期刊介绍： Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way. Published Bi-monthly Published for the Australian Mathematical Society

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