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Note on some greatest common divisor matrices

100%

Lindqvist P., Seip K.

Acta Arithmetica

1998

tom 84

nr 2

149-154

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.

Convergence of series of dilated functions and spectral norms of GCD matrices

81%

Aistleitner C., Berkes I., Seip K., Weber M.

Acta Arithmetica

2015

tom 168

nr 3

221-246

We establish a connection between the L² norm of sums of dilated functions whose jth Fourier coefficients are $𝓞(j^{-α})$ for some α ∈ (1/2,1), and the spectral norms of certain greatest common divisor (GCD) matrices. Utilizing recent bounds for these spectral norms, we obtain sharp conditions for the convergence in L² and for the almost everywhere convergence of series of dilated functions.

Ograniczanie wyników

2 Acta Arithmetica

2 Seip K.

1 Aistleitner C.

1 Berkes I.

1 Lindqvist P.

1 Weber M.

1 2015

1 1998

Wyniki wyszukiwania

Note on some greatest common divisor matrices

Convergence of series of dilated functions and spectral norms of GCD matrices