The group of squarefree integers

被引：7

作者：

Hilberdink, Titus ^{[1
]}

机构：

[1] Univ Reading, Dept Math, Reading RG6 6AX, Berks, England

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2014年 / 457卷

关键词：

Squarefree numbers; Gcd and lcm; Character group; SUMS;

D O I：

10.1016/j.laa.2014.05.037

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the consequences of the elementary observation that the squarefree numbers form a group under the operation lcm/gcd. In particular, we discuss the characters on this group, one of which is the Mobius function, as well as the finite subgroups D(k) formed from the divisors of a given squarefree integer k. We show further how a convolution, naturally based on this operation, leads to the factorization of various arithmetical matrices and the evaluation of the eigenvalues. We discuss briefly the associated L-functions. Finally, we generalize the operation to other subsets of N. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：383 / 399

页数：17

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