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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions
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by Philippe Biane, Jim Pitman and Marc Yor PDF
Bull. Amer. Math. Soc. 38 (2001), 435-465 Request permission


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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Additional Information
  • Philippe Biane
  • Affiliation: CNRS, DMA, 45 rue d’Ulm 75005 Paris, France
  • Email:
  • Jim Pitman
  • Affiliation: Department of Statistics, University of California, 367 Evans Hall #3860, Berkeley, CA 94720-3860
  • MR Author ID: 140080
  • Email: pitman@stat.Berkeley.EDU
  • Marc Yor
  • Affiliation: Laboratoire de Probabilités, Université Pierre et Marie Curie, 4 Place Jussieu F-75252, Paris Cedex 05, France
  • Received by editor(s): October 19, 1999
  • Received by editor(s) in revised form: January 29, 2001
  • Published electronically: June 12, 2001
  • Additional Notes: Supported in part by NSF grants DMS-97-03961 and DMS-00071448
  • © Copyright 2001 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 38 (2001), 435-465
  • MSC (2000): Primary 11M06, 60J65, 60E07
  • DOI:
  • MathSciNet review: 1848256