Fourier-Stieltjes coefficients of the Minkowski question mark function

Details Fourier-Stieltjes coefficients of the Minkowski question mark function Fourier-Stieltjes coefficients of the Minkowski question mark function

2010-08-24

arxiv.org/abs/1008.4014v3

Mathematics

Classical Analysis and ODEs

15 pages, 4 figures. To appear in: Analytic and Probabilistic Methods in Number Theory, Proceedings of the Fifth Intern. Conf.

Scientific paper

In this paper we investigate the Fourier-Stieltjes coefficients of the Minkowski question mark function. In 1943, R. Salem asked whether these coefficients vanish at infinity. We propose the conjecture which implies the affirmative answer to Salem's problem. Further, we prove infinite linear identities among these Fourier-Stieltjes coefficients. We also provide a method to numerically calculate special values at integers of the associated zeta function with a high precision (more than 30 digits).

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