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
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.References
- Dennis A. Hejhal, The Selberg trace formula for $\textrm {PSL}(2,R)$. Vol. I, Lecture Notes in Mathematics, Vol. 548, Springer-Verlag, Berlin-New York, 1976. MR 0439755
- J. Korevaar, A century of complex Tauberian theory, Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 4, 475–531. MR 1920279, DOI 10.1090/S0273-0979-02-00951-5
- A. M. Nikitin, The Ihara-Selberg zeta function of a finite graph and symbolic dynamics, Algebra i Analiz 13 (2001), no. 5, 134–149 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 13 (2002), no. 5, 809–820. MR 1882866
- A. B. Venkov and A. M. Nikitin, The Selberg trace formula, Ramanujan graphs and some problems in mathematical physics, Algebra i Analiz 5 (1993), no. 3, 1–76 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 5 (1994), no. 3, 419–484. MR 1239898
- Michel Loève, Probability theory. I, 4th ed., Graduate Texts in Mathematics, Vol. 45, Springer-Verlag, New York-Heidelberg, 1977. MR 0651017
- Yiannis N. Petridis, Spectral deformations and Eisenstein series associated with modular symbols, Int. Math. Res. Not. 19 (2002), 991–1006. MR 1903327, DOI 10.1155/S1073792802111159
- Y. N. Petridis and M. S. Risager, Modular symbols have a normal distribution, Geom. Funct. Anal. 14 (2004), no. 5, 1013–1043. MR 2105951, DOI 10.1007/s00039-004-0481-8
- 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.
- Morten S. Risager, On the distribution of modular symbols for compact surfaces, Int. Math. Res. Not. 41 (2004), 2125–2146. MR 2078851, DOI 10.1155/S1073792804132352
- I. Rivin, Growth in free groups (and other stories), arXiv:math.CO/9911076.
- Jean-Pierre Serre, Trees, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003. Translated from the French original by John Stillwell; Corrected 2nd printing of the 1980 English translation. MR 1954121
- Richard Sharp, Local limit theorems for free groups, Math. Ann. 321 (2001), no. 4, 889–904. MR 1872533, DOI 10.1007/s002080100258
- Audrey Terras, Fourier analysis on finite groups and applications, London Mathematical Society Student Texts, vol. 43, Cambridge University Press, Cambridge, 1999. MR 1695775, DOI 10.1017/CBO9780511626265
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
- MR Author ID: 740566
- Email: risager@imf.au.dk
- 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: https://doi.org/10.1090/S0002-9939-05-08074-3
- MathSciNet review: 2196031