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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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.


The importance of the Selberg integral
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by Peter J. Forrester and S. Ole Warnaar PDF
Bull. Amer. Math. Soc. 45 (2008), 489-534 Request permission


It has been remarked that a fair measure of the impact of Atle Selberg’s work is the number of mathematical terms that bear his name. One of these is the Selberg integral, an $n$-dimensional generalization of the Euler beta integral. We trace its sudden rise to prominence, initiated by a question to Selberg from Enrico Bombieri, more than thirty years after its initial publication. In quick succession the Selberg integral was used to prove an outstanding conjecture in random matrix theory and cases of the Macdonald conjectures. It further initiated the study of $q$-analogues, which in turn enriched the Macdonald conjectures. We review these developments and proceed to exhibit the sustained prominence of the Selberg integral as evidenced by its central role in random matrix theory, Calogero–Sutherland quantum many-body systems, Knizhnik–Zamolodchikov equations, and multivariable orthogonal polynomial theory.
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Additional Information
  • Peter J. Forrester
  • Affiliation: Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia
  • MR Author ID: 68170
  • S. Ole Warnaar
  • Affiliation: Department of Mathematics, The University of Queensland, St Lucia, Queensland 4072, Australia
  • MR Author ID: 269674
  • Received by editor(s): March 21, 2008
  • Received by editor(s) in revised form: April 21, 2008
  • Published electronically: July 2, 2008
  • © Copyright 2008 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 45 (2008), 489-534
  • MSC (2000): Primary 00-02, 33-02
  • DOI:
  • MathSciNet review: 2434345