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Digital Sums and Divide-and-Conquer Recurrences: Fourier Expansions and Absolute Convergence

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Abstract

We propose means for computing the Fourier expansions of periodic functions appearing in higher moments of the sum-of-digits function and in the solutions of some divide-and-conquer recurrences. The expansions are shown to be absolutely convergent. We also give a new approach to efficiently compute numerically the coefficients involved to high precision.

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  1. Institut für Mathematik A, Technische Universität Graz, Steyrergasse 30 8010, Graz, Austria

    Peter J. Grabner & Hsien-Kuei Hwang

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  1. Peter J. Grabner
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  2. Hsien-Kuei Hwang
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Correspondence to Peter J. Grabner.

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Grabner, P., Hwang, HK. Digital Sums and Divide-and-Conquer Recurrences: Fourier Expansions and Absolute Convergence. Constr Approx 21, 149–179 (2005). https://doi.org/10.1007/s00365-004-0561-x

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  • DOI: https://doi.org/10.1007/s00365-004-0561-x

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