与Jacobi θ和黎曼ζ函数及布朗漂移有关的概率定律
Probability laws related to the Jacobi theta and Riemann zeta function and Brownian excursions
摘要：
本文回顾了已知的结果连接黎曼的整表示他的zeta函数，涉及雅可比的θ函数及其衍生物，一些特殊的概率定律，独立指数变量的总和。这些法律有关的一维布朗运动和高维贝塞尔过程。我们给出了这些概率律的一些特征，以及与这些概率律有关的黎曼zeta函数的一些近似。
英文摘要：
This paper reviews known results which connect Riemann's integral representations of his zeta function, involving Jacobi's theta function and its derivatives, to some particular probability laws governing sums of independent exponential variables. These laws are related to one-dimensional Brownian motion and to higher dimensional Bessel processes. We present some characterizations of these probability laws, and some approximations of Riemann's zeta function which are related to these laws.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
