Discrete logarithms in free groups
Authors:
Yiannis N. Petridis and Morten S. Risager
Journal:
Proc. Amer. Math. Soc. 134 (2006), 10031012
MSC (2000):
Primary 05C25; Secondary 11M36
Published electronically:
October 5, 2005
MathSciNet review:
2196031
Fulltext PDF Free Access
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Abstract: For the free group on generators we prove that the discrete logarithm is distributed according to the standard Gaussian when the logarithm is renormalized appropriately.
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 D. Hejhal, The Selberg trace formula for . Vol. 1. Lecture Notes in Mathematics, 1001. SpringerVerlag, Berlin, 1976, vi+516pp. MR 0439755 (55:12641)
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 J. Korevaar, A century of complex Tauberian theory. Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 4, 475531 (electronic). MR 1920279 (2003g:40004)
 3.
 A. M. Nikitin, The IharaSelberg zeta function of a finite graph and symbolic dynamics, Algebra i Analiz 13 (2001), no. 5, 134149; translation in St. Petersburg Math. J. 13 (2002), no. 5, 809820. MR 1882866 (2003f:11137)
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 Y. N. Petridis, M. S. Risager, The distribution of values of the Poincaré pairing for hyperbolic Riemann surfaces, J. Reine Ang. Mat. 579 (2005), 159173.
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 M. S. Risager, On the distribution of modular symbols for compact surfaces, Internat. Math. Res. Notices 2004, No. 41, 21252146. MR 2078851
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 I. Rivin, Growth in free groups (and other stories), arXiv:math.CO/9911076.
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 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)
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 R. Sharp, Local limit theorems for free groups, J. Math. Ann. 321 (2001), 4, p. 889904. MR 1872533 (2002k:20039)
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 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 104681589
Address at time of publication:
The Graduate Center, Mathematics Ph.D. Program, 365 Fifth Avenue, Room 4208 New York, New York 100164309
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:
http://dx.doi.org/10.1090/S0002993905080743
PII:
S 00029939(05)080743
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. 600073334, and NSF grant DMS 0401318
Communicated by:
WenChing Winnie Li
Article copyright:
© Copyright 2005
American Mathematical Society
