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Journal of Modern Dynamics (JMD)
 

Quadratic irrationals and linking numbers of modular knots
Pages: 539 - 561, Issue 4, October 2012

doi:10.3934/jmd.2012.6.539      Abstract        References        Full text (241.8K)           Related Articles

Dubi Kelmer - Boston College, Department of Mathematics, Chestnut Hill, MA 02467, United States (email)

1 E. Artin, Ein mechanisches System mit quasiergodischen Bahnen, Hamb. Math. Abh., 3 (1924), 170-177.
2 W. Duke, Hyperbolic distribution problems and half-integral weight Maass forms, Invent. Math., 92 (1988), 73-90.       
3 I. Efrat, Dynamics of the continued fraction map and the spectral theory of $SL(2,\mathbf Z)$, Invent. Math., 114 (1993), 207-218.       
4 É. Ghys, Knots and dynamics, in "International Congress of Mathematicians," Vol. I, Eur. Math. Soc., Zürich, (2007), 247-277.       
5 D. A. Hejhal, "The Selberg Trace Formula for $PSL(2, \mathbf R)$," Vol. 2, Lecture Notes in Mathematics, Vol. 1001, Springer-Verlag, Berlin, 1983.       
6 T. Kato, "A Short Introduction to Perturbation Theory for Linear Operators," Springer-Verlag, New York-Berlin, 1982.       
7 J. Korevaar, "Tauberian Theory. A Century of Developments," Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Vol. 329, Springer-Verlag, Berlin, 2004.       
8 A. Katsuda and T. Sunada, Closed orbits in homology classes, Inst. Hautes Études Sci. Publ. Math., No. 71 (1990), 5-32.       
9 S. P. Lalley, Closed geodesics in homology classes on surfaces of variable negative curvature, Duke Math. J., 58 (1989), 795-821.       
10 D. H. Mayer, On a $\zeta$ function related to the continued fraction transformation, Bull. Soc. Math. France, 104 (1976), 195-203.       
11 _____, The thermodynamic formalism approach to Selberg's zeta function for $PSL(2,\mathbf Z)$, Bull. Amer. Math. Soc. (N.S.), 25 (1991), 55-60.       
12 C. J. Mozzochi, Linking numbers of modular geodesics, preprint, (2010).
13 M. Pollicott, Distribution of closed geodesics on the modular surface and quadratic irrationals, Bull. Soc. Math. France, 114 (1986), 431-446.       
14 _____, Homology and closed geodesics in a compact negatively curved surface, Amer. J. Math., 113 (1991), 379-385.       
15 R. Phillips and P. Sarnak, Geodesics in homology classes, Duke Math. J., 55 (1987), 287-297.       
16 H. Rademacher and E. Grosswald, "Dedekind Sums," The Carus Mathematical Monographs, No. 16, The Mathematical Association of America, Washington, D. C., 1972.       
17 P. Sarnak, Class numbers of indefinite binary quadratic forms, J. Number Theory, 15 (1982), 229-247.       
18 _____, Reciprocal geodesics, in "Analytic Number Theory," Clay Math. Proc., 7, Amer. Math. Soc., Providence, RI, (2007), 217-237.       
19 _____, Linking numbers of modular knots, Commun. Math. Anal., 8 (2010), 136-144.       
20 C. Series, The modular surface and continued fractions, J. London Math. Soc. (2), 31 (1985), 69-80.       
21 S. Zelditch, Trace formula for compact $\Gamma\backslash PSL_2(\mathbf R)$ and the equidistribution theory of closed geodesics, Duke Math. J., 59 (1989), 27-81.       

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