Séminaire du 23 septembre 2002,Hsien Kuei Hwang, Academia Sinica, Taiwan.
Digital sums and divide-and-conquer recurrences: Fourier expansions and absolute convergence
We propose means of 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 showed to be absolutely convergent. We also give a new approach to efficiently computing numerically the coefficients involved to high precision.