%0 Journal Article %1 bpy99z %A Biane, Philippe %A Pitman, Jim %A Yor, Marc %D 2001 %J Bull. Amer. Math. Soc. %K Brownian_excursions Dept_Mathematics_Berkeley Dept_Statistics_Berkeley Jacobi_theta_function Riemmann_zeta_function myown %P 435-465 %T Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions %U http://www.ams.org/journal-getitem?pii=S0273-0979-01-00912-0 %V 38 %X 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.

@article{bpy99z, 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.}, added-at = {2008-01-20T02:39:38.000+0100}, arxiv = {math.PR/9912170}, author = {Biane, Philippe and Pitman, Jim and Yor, Marc}, bibnumber = {105}, biburl = {https://www.bibsonomy.org/bibtex/2b439417f19ee3152968e5e713b5a6d39/pitman}, interhash = {99f7fe340e04a033b14ff91cbb92a15c}, intrahash = {b439417f19ee3152968e5e713b5a6d39}, journal = {Bull. Amer. Math. Soc.}, keywords = {Brownian_excursions Dept_Mathematics_Berkeley Dept_Statistics_Berkeley Jacobi_theta_function Riemmann_zeta_function myown}, mrclass = {11M06 (11K99 60E07 60J65)}, mrnumber = {MR1848256}, pages = {435-465}, timestamp = {2010-10-30T22:51:57.000+0200}, title = {{Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions}}, url = {http://www.ams.org/journal-getitem?pii=S0273-0979-01-00912-0}, volume = 38, year = 2001, znumber = {01663205} }