Analysis of stochastic processes on the adeles

构造了Adeles上的马尔可夫过程，分析了退出时间的分布以及退出时过程的p-分支的p-进范数。用有限积分Adeles刻画过程的出射时间分布。Riemann的Zeta和其他函数的公式，用欧拉乘积表示过程的退出时间和p-分量在退出时间的p-进范数。与黎曼Zeta函数在一点的值及其复共轭或其实部相关的函数方程。

Construction of Markov processes on the adeles, and analysis of the distribution of the exit time from the p-adic integer ring, and the p-adic norm of the p-component of the processes at the exit time. Description of the distribution of the exit time of the adelic processes from the finite integral adeles. Formulae for Riemann's zeta and other functions with Euler product representations in terms of the exit time of the processes and the p-adic norm of the p-component at the exit time. Functional equations relating the values of Riemann's zeta function at a point and its complex conjugates or its real part.