2001/11/08 by Matilde Marcolli, Marcolli, Matilde
Mathematics · #37D35 11M36 10D15 46L89 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.DS #math.NT #msc:10D15 #msc:11M36 #msc:37D35 #msc:46L89
paper · pdf · doi:10.48550/arxiv.math/0111093
25 pages LaTeX
arxiv created 2001/11/08 · openalex publication_date 2001/11/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper consists of variations upon the theme of limiting modular symbols. Topics covered are: an expression of limiting modular symbols as Birkhoff averages on level sets of the Lyapunov exponent of the shift of the continued fraction, a vanishing theorem depending on the spectral properties of a generalized Gauss-Kuzmin operator, the construction of certain non-trivial homology classes associated to non-closed geodesics on modular curves, certain Selberg zeta functions and C^* algebras related to shift invariant sets.