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arXiv · 2310.12468

Higher-Weight Limiting Modular Symbols

Jane Panangaden
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Abstract

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 Kesseb\"ohmer and Stratmann in the weight-2 case.

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Jane Panangaden. 2023-10-19. Higher-Weight Limiting Modular Symbols. https://arxiv.org/abs/2310.12468

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