  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).
