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Higher-Weight Limiting Modular Symbols

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Jane Panangaden

Number Theory · Submitted 19 Oct 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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arXiv ID2310.12468 (version 1)
Pith IDUYGCN37D, Pith's permanent record of this paper and its review
CitationJane Panangaden. "Higher-Weight Limiting Modular Symbols." arXiv:2310.12468 (2023). https://pith.science/paper/UYGCN37D
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The compiled record

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,297 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.95 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We begin with the higher-weight modular symbols introduced by Shokurov, which generalize Manin's weight-2 modular symbols. background 0.99 0.14 0.03 asserted 0.98
s1 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. contribution 0.88 0.93 0.09 asserted 0.99
s2 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. background 0.86 0.10 0.06 asserted 1.00
s3 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. result 0.97 0.94 0.59 asserted 1.00
s4 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. method 1.00 0.54 0.07 asserted 0.96

What kind of paper the classifier reports this is: theoretical result 0.95 · evidence from proof or derivation 1.00.

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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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