  The Minkowski question mark function ?(x) arises as a real distribution of
rationals in the Farey tree. We examine the generating function of moments of
?(x). It appears that the generating function is a direct dyadic analogue of
period functions for Maass wave forms and it is defined in the cut plane
C(0,infinity). The exponential generating function satisfies the integral
equation with kernel being the Bessel function. The solution of this integral
equation leads to the definition of dyadic eigenfunctions, arising from a
certain Hilbert-Schmidt operator. Finally, we describe p-adic distribution of
rationals in the Stern-Brocot tree. Surprisingly, the Eisenstein series G_1(z)
does manifest in both real and p-adic cases.
