Dirichlet matrices: Determinants, permanents and the Factorisatio Numerorum problem

被引：3

作者：

de Camargo, Andre Pierro ^{[1
]}

机构：

[1] Fed Univ ABC Reg, Ctr Math Cognit & Comp Sci, Sao Paulo, Brazil

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2021年 / 628卷

关键词：

Dirichlet matrices; Redheffer matrices; Mertens function; Factorisatio Numerorum; Riemann hypothesis; NUMBER;

D O I：

10.1016/j.laa.2021.07.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Dirichlet matrices are strongly connected to some important problems in Number Theory, such as the Prime Number Theorem, the Riemann Hypothesis and Kalmar's Factorisatio Numerorum problem. In this note, we obtain some recurrences for the determinants and permanents of Dirichlet matrices that allows us to obtain information about the asymptotic behavior of the permanents of certain classes of Dirichlet matrices. A generalization of Kalmar's Factorisatio Numerorum problem is obtained. (C) 2021 Elsevier Inc. All rights reserved.

引用

页码：115 / 129

页数：15

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