On the norms of GCD matrices (Q1848705)

A greatest common divisor (GCD) matrix \(A=(a_{ij})\) is defined as \(a_{ij}=\gcd(i,j)\). The general form of almost GCD Cauchy-Toeplitz and almost GCD Cauchy-Hankel matrices \(T=(t_{ij})\) and \(H=(h_{ij})\) are respectively defined by \[ t_{ij}=\begin{cases} a,&i=j\\ \frac{\gcd(i,j)}{i-j},&i\neq j\end{cases}\quad\text{and}\quad h_{ij}=\frac{\gcd(i,j)}{i+j} \] where \(a\) is a real number and \(i,j=1,2,\dots,n\). In this paper, the bounds for the \(\ell_p\) norms and the Euclidean norm of almost GCD Cauchy-Toeplitz and almost GCD Cauchy-Hankel matrices are obtained.