欧拉函数
整数(计算机科学)
数学
正交性
拉马努詹之和
特征向量
整数矩阵
最大公约数
欧拉公式
组合数学
除数(代数几何)
数论
Dirichlet分布
基质(化学分析)
纯数学
对称矩阵
计算机科学
数学分析
物理
几何学
非负矩阵
复合材料
边值问题
材料科学
程序设计语言
量子力学
作者
Karl Dilcher,Kurt Girstmair
标识
DOI:10.1080/00029890.2022.2026165
摘要
For each integer n≥3 we define a specific symmetric integer matrix of size φ(n)/2. We then explicitly describe all positive and negative integer powers, as well as fractional powers, of each of these matrices; their eigenvalues also appear and play an important role. All this is based on an orthogonality relation for odd Dirichlet characters which, in turn, leads to a diagonalization. In the course of this article, various other number-theoretic objects make their appearance, including the Euler and Jordan totient functions, Möbius inversion, and the divisor function.
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