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

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

1999-12-21

arxiv.org/abs/math/9912170v1

Mathematics

Probability

LaTeX; 40 pages; review paper

Scientific paper

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.

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