Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions-Reference-Cited by-同舟云学术

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

Published:2001-06-12 Issue:4 Volume:38 Page:435-465
ISSN:0273-0979
Container-title:Bulletin of the American Mathematical Society
language:en
Short-container-title:Bull. Amer. Math. Soc.

Author:

Biane Philippe,Pitman Jim,Yor Marc

Abstract

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/bull/2001-38-04/S0273-0979-01-00912-0/S0273-0979-01-00912-0.pdf

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