Note on some greatest common divisor matrices
Tom 84 / 1998
Acta Arithmetica 84 (1998), 149-154
DOI: 10.4064/aa-84-2-149-154
Streszczenie
Some quadratic forms related to "greatest common divisor matrices" are represented in terms of L²-norms of rather simple functions. Our formula is especially useful when the size of the matrix grows, and we will study the asymptotic behaviour of the smallest and largest eigenvalues. Indeed, a sharp bound in terms of the zeta function is obtained. Our leading example is a hybrid between Hilbert's matrix and Smith's matrix.
