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

Christoph Aistleitner, István Berkes, Kristian Seip, Michel Weber (2015)

Acta Arithmetica

We establish a connection between the L² norm of sums of dilated functions whose jth Fourier coefficients are ( 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.

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