Displaying similar documents to “Anisotropic complex structure on the pseudo-Euclidean Hurwitz pairs”

Note on some greatest common divisor matrices

Peter Lindqvist, Kristian Seip (1998)

Acta Arithmetica

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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.

Evaluation of divisor functions of matrices

Gautami Bhowmik (1996)

Acta Arithmetica

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1. Introduction. The study of divisor functions of matrices arose legitimately in the context of arithmetic of matrices, and the question of the number of (possibly weighted) inequivalent factorizations of an integer matrix was asked. However, till now only partial answers were available. Nanda [6] evaluated the case of prime matrices and Narang [7] gave an evaluation for 2×2 matrices. We obtained a recursion in the size of the matrices and the weights of the divisors [1,2] which helped...