Continued Fractions , Modular Symbols , and Non { Commutative Geometry

  title={Continued Fractions , Modular Symbols , and Non \{ Commutative Geometry},
  author={Yuri I. Manin and Matilde Marcolli},
Using techniques introduced by D. Mayer, we prove an extension of the classical Gauss{Kuzmin theorem about the distribution of continued fractions, which in particular allows one to take into account some congruence properties of successive convergents. This result has an application to the Mixmaster Universe model in general relativity. We then study some averages involving modular symbols and show that Dirichlet series related to modular forms of weight 2 can be obtained by integrating… CONTINUE READING
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