ON THE DISTRIBUTION OF THE PARTIAL SUM OF EULER'S TOTIENT FUNCTION IN RESIDUE CLASSES

被引：1
|
作者：
Lamzouri, Youness [1 ]
Phaovibul, M. Tip [1 ]
Zaharescu, Alexandru [1 ]
机构：
[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA
来源：
COLLOQUIUM MATHEMATICUM | 2011年 / 123卷 / 01期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Euler's totient function; distribution in residue classes;
D O I：
10.4064/cm123-1-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigate the distribution of Phi(n) = 1 + Sigma(n)(i=1) phi(i) (which counts the number of Farey fractions of order n) in residue classes. While numerical computations suggest that Phi(n) is equidistributed modulo q if q is odd, and is equidistributed modulo the odd residue classes modulo q when q is even, we prove that the set of integers n such that Phi(n) lies in these residue classes has a positive lower density when q = 3,4. We also provide a simple proof, based on the Selberg-Delange method, of a result of T. Dence and C. Pomerance on the distribution of phi(n) modulo 3.
引用
收藏
页码：115 / 127
页数：13
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