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Discrete logarithms in free groups


Authors: Yiannis N. Petridis and Morten S. Risager
Journal: Proc. Amer. Math. Soc. 134 (2006), 1003-1012
MSC (2000): Primary 05C25; Secondary 11M36
DOI: https://doi.org/10.1090/S0002-9939-05-08074-3
Published electronically: October 5, 2005
MathSciNet review: 2196031
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Abstract: 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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  • 1. D. Hejhal, The Selberg trace formula for ${\rm PSL}(2,\,R)$. Vol. 1. Lecture Notes in Mathematics, 1001. Springer-Verlag, Berlin, 1976, vi+516pp. MR 0439755 (55:12641)
  • 2. J. Korevaar, A century of complex Tauberian theory. Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 4, 475-531 (electronic). MR 1920279 (2003g:40004)
  • 3. A. M. Nikitin, The Ihara-Selberg zeta function of a finite graph and symbolic dynamics, Algebra i Analiz 13 (2001), no. 5, 134-149; translation in St. Petersburg Math. J. 13 (2002), no. 5, 809-820. MR 1882866 (2003f:11137)
  • 4. A. M. Nikitin and A. B. Venkov, The Selberg trace formula, Ramanujan graphs and some problems in mathematical physics. (Russian), Algebra i Analiz 5 (1993), no. 3, 1-76; translation in St. Petersburg Math. J. 5 (1994), no. 3, 419-484. MR 1239898 (94m:11066)
  • 5. M. Loève, Probability theory. I, Fourth edition, Springer, New York, 1977. MR 0651017 (58:31324a)
  • 6. Y. N. Petridis, Spectral deformations and Eisenstein Series Associated with Modular Symbols. Internat. Math. Res. Notices 2002, no. 19, 991-1006.MR 1903327 (2003h:11057)
  • 7. Y. N. Petridis, M. S. Risager, Modular symbols have a normal distribution, Geom. Funct. Anal. 14 (2004), no. 5, 1013-1043. MR 2105951
  • 8. Y. N. Petridis, M. S. Risager, The distribution of values of the Poincaré pairing for hyperbolic Riemann surfaces, J. Reine Ang. Mat. 579 (2005), 159-173.
  • 9. M. S. Risager, On the distribution of modular symbols for compact surfaces, Internat. Math. Res. Notices 2004, No. 41, 2125-2146. MR 2078851
  • 10. I. Rivin, Growth in free groups (and other stories), arXiv:math.CO/9911076.
  • 11. J.-P. Serre, Trees, Translated from the French original by John Stillwell, Corrected 2nd printing of the 1980 English translation, Springer, Berlin, 2003. MR 1954121 (2003m:20032)
  • 12. R. Sharp, Local limit theorems for free groups, J. Math. Ann. 321 (2001), 4, p. 889-904. MR 1872533 (2002k:20039)
  • 13. A. Terras, Fourier analysis on finite groups and applications, Cambridge Univ. Press, Cambridge, 1999. MR 1695775 (2000d:11003)

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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: petridis@comet.lehman.cuny.edu

Morten S. Risager
Affiliation: Department of Mathematical Sciences, University of Aarhus, Ny Munkegade Building 530, 8000 Aarhus, Denmark
Email: risager@imf.au.dk

DOI: https://doi.org/10.1090/S0002-9939-05-08074-3
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
Article copyright: © Copyright 2005 American Mathematical Society

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