The Fibonacci--Redheffer matrix and its properties

TL;DR

This paper introduces a Fibonacci-based Redheffer matrix, explores its determinant and spectral properties, and discusses broader generalizations, asymptotic behaviors, and connections to the Riemann hypothesis.

Contribution

It defines a new Fibonacci-Redheffer matrix, analyzes its properties, and links these findings to number theory and the Riemann hypothesis.

Findings

Determinant and spectral properties of the Fibonacci-Redheffer matrix are characterized.

Generalizations of Redheffer-type matrices are studied with number-theoretic examples.

Asymptotic results and a new expression related to the Riemann hypothesis are presented.

Abstract

A Redheffer--type matrix with Fibonacci entries is defined, and the determinant and spectral properties of this matrix are studied. Also, more general Redheffer--type matrices are considered and intriguing number-theoretic examples are illustrated. Furthermore, several asymptotic results are discussed and a new expression related to the Riemann hypothesis is presented.