arXiv:math/9912170 Abstract

arXiv:math/9912170 [math.PR]Abstract References Reviews Resources

Probability laws related to the Jacobi theta and Riemann zeta function and Brownian excursions

Published 1999-12-21Version 1

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.

Comments: LaTeX; 40 pages; review paper

Categories: math.PR, math.CA

Subjects: 11M06, 60J65, 60E07

Keywords: riemann zeta function, probability laws, jacobi theta, brownian excursions, higher dimensional bessel processes

Related articles: Most relevant | Search more

arXiv:math/0511517 [math.PR] (Published 2005-11-21)

Exponential functionals of Brownian motion, I: Probability laws at fixed time

Hiroyuki Matsumoto, Marc Yor

arXiv:2102.10095 [math.PR] (Published 2021-02-19)

Brownian bridge expansions for Lévy area approximations and particular values of the Riemann zeta function

James Foster, Karen Habermann

arXiv:1706.08462 [math.PR] (Published 2017-06-26)