Fourier-Stieltjes coefficients of the Minkowski question mark function
arXiv:1008.4014
Abstract
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).
15 pages, 4 figures. Typos fixed (e.g., in the formula (7)). To appear in: Analytic and Probabilistic Methods in Number Theory, Proceedings of the Fifth Intern. Conf. in Honour of J. Kubilius, Palanga, Lithuania, 4-10 September 2011
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- Asymptotic formula for the moments of Minkowski question mark function in the interval [0,1]