标题： Minkowski 问号函数的矩：二进制周期函数 显示英文标题

标题： The moments of Minkowski question mark function: the dyadic period function

摘要： 闵可夫斯基问号函数 ?(x) 在法里树中作为有理数的实分布出现。我们研究 ?(x) 的矩生成函数。看起来，该生成函数是马斯波函数周期函数的直接二进制类比，并在割平面 C(0,无穷大) 中定义。指数生成函数满足积分方程，其核为贝塞尔函数。该积分方程的解导致了从某个希尔伯特-施密特算子中产生的二进制本征函数的定义。最后，我们描述了斯特恩-布罗科特树中有理数的p进分布。令人惊讶的是，爱森斯坦级数 G_1(z) 在实数和p进情形中都表现出来。 显示英文摘要

摘要： 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.