[1]朱玉清,连冬艳,刁天博,等.与算术函数相关联的广义GCD矩阵的行列式(英)[J].四川师范大学学报(自然科学版),2018,(01):72-76.[doi:10.3969/j.issn.1001-8395.2018.01.014]
 ZHU Yuqing,LIAN Dongyan,DIAO Tianbo,et al.Determinants of Generalized GCD Matrices Associated with Arithmetic Functions[J].Journal of SichuanNormal University,2018,(01):72-76.[doi:10.3969/j.issn.1001-8395.2018.01.014]
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与算术函数相关联的广义GCD矩阵的行列式(英)()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2018年01期
页码:
72-76
栏目:
基础理论
出版日期:
2017-12-06

文章信息/Info

Title:
Determinants of Generalized GCD Matrices Associated with Arithmetic Functions
文章编号:
1001-8395(2018)01-0072-05
作者:
朱玉清1 连冬艳1 刁天博1 胡双年12
1.南阳理工学院 数学与统计学院, 河南 南阳 473004; 2.郑州大学 数学与统计学院, 河南 郑州 450001
Author(s):
ZHU Yuqing1 LIAN Dongyan1 DIAO Tianbo1 HU Shuangnian12
1.College of Mathematics and Statistics, Nanyang Institute of Technology, Nanyang 473004, Henan; 2.College of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, Henan
关键词:
GCD矩阵 算术函数 行列式
Keywords:
GCD matrix arithmetic function determinant
分类号:
O156.3; O153.4
DOI:
10.3969/j.issn.1001-8395.2018.01.014
文献标志码:
A
摘要:
设S={x1,…,xn}是由n个元素组成的正整数集合,f是一个算术函数.用((^overf)(S))表示一个n×n的矩阵,其(i,j)项为∑d|xid∈Sf(d)-∑d|(xi,xj)d∈Sf(d),用((-overf)(S))表示另一个n×n的矩
Abstract:
Let S={x1,…,xn} be a set of n distinct positive integers and f be an arithmetic function. By ((^overf)(S))(resp. ((-overf)(S))), we denote the n×n matrix whose i,j-entry is ∑d|xid∈Sf(d)-∑d|(xi,xj)d∈Sf(d)(resp. ∑x∈Sf(x)-∑d|xid∈Sf(d)-∑d|xjd∈Sf(d)+∑d|(xi,xj)d∈Sf(d)). In this paper, we first investigate the structures of the matrices ((^overf)(S)), ((-overf)(S)), and then give the formulae for the determinants of these matrices. Our result generalizes the result given by Bege in 2010.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2016-10-10
基金项目:中国博士后基金(2016M602251)和河南省高校重点项目(17A110010)
第一作者简介:朱玉清(1967—),女,教授,主要从事数论的研究,E-mail:1065396967@qq.com
更新日期/Last Update: 2017-12-07