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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Discrete logarithms in free groups
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by Yiannis N. Petridis and Morten S. Risager PDF
Proc. Amer. Math. Soc. 134 (2006), 1003-1012 Request permission


For the free group on $n$ generators we prove that the discrete logarithm is distributed according to the standard Gaussian when the logarithm is renormalized appropriately.
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Additional Information
  • Yiannis N. Petridis
  • Affiliation: Department of Mathematics and Computer Science, City University of New York, Lehman College, 250 Bedford Park Boulevard, West Bronx, New York 10468-1589
  • Address at time of publication: The Graduate Center, Mathematics Ph.D. Program, 365 Fifth Avenue, Room 4208 New York, New York 10016-4309
  • Email:
  • Morten S. Risager
  • Affiliation: Department of Mathematical Sciences, University of Aarhus, Ny Munkegade Building 530, 8000 Aarhus, Denmark
  • MR Author ID: 740566
  • Email:
  • Received by editor(s): August 9, 2004
  • Received by editor(s) in revised form: November 12, 2004
  • Published electronically: October 5, 2005
  • Additional Notes: The first author was partially supported by PSC CUNY Research Award, No. 60007-33-34, and NSF grant DMS 0401318
  • Communicated by: Wen-Ching Winnie Li
  • © Copyright 2005 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 1003-1012
  • MSC (2000): Primary 05C25; Secondary 11M36
  • DOI:
  • MathSciNet review: 2196031