2023/10/19 by Jane Panangaden, Panangaden, Jane
Engineering · Mathematics · #Arithmetic #Combinatorics #Computer science #Confusion #Discrete mathematics #Engineering #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Geometry #Homotopy and Cohomology in Algebraic Topology #Irrational number #Limit (mathematics) #Limiting #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Mathematical analysis #Mathematics #Modular design #Modular form #Modular group #Number Theory (math.NT) #Pure mathematics
paper · pdf · doi:10.48550/arxiv.2310.12468
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We begin with the higher-weight modular symbols introduced by Shokurov, which generalize Manin's weight-2 modular symbols. We then define higher-weight limiting modular symbols associated to vertical geodesics with one endpoint at an irrational real number, by means of a limiting procedure on Shokurov's modular symbols. These are analogous to the Manin-Marcolli limiting modular symbols for the weight-2 case, which are given by a similar limiting procedure on the Manin modular symbols. We show that the limit defining the higher-weight limiting modular symbol is equivalent everywhere to a limit given by approximating the irrational endpoint by its continued fraction expansion. This is done by means of shifting to a coding space, as in the approach of Kesseböhmer and Stratmann in the weight-2 case.