Displaying similar documents to “Evaluation of divisor functions of matrices”

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.

Luzin and anti-Luzin almost disjoint families

Judith Roitman, Lajos Soukup (1998)

Fundamenta Mathematicae

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Under M A ω 1 every uncountable almost disjoint family is either anti-Luzin or has an uncountable Luzin subfamily. This fails under CH. Related properties are also investigated.