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Spectre automorphe des vari\'et\'es hyperboliques et applications topologiques

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N. Bergeron, L. Clozel

Number Theory · Submitted 17 Nov 2004

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

The authors' main claim We prove Selberg type theorems on the first eigenvalue of the laplacian on differential forms.

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arXiv IDmath/0411385 (version 1)
Pith IDP4J7NB4O, Pith's permanent record of this paper and its review
CitationL. Clozel, N. Bergeron. "Spectre automorphe des vari\'et\'es hyperboliques et applications topologiques." arXiv:math/0411385 (2004). https://pith.science/paper/P4J7NB4O
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,157 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.12 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.07 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

This book is made of two parts. The first is concerned with the differential form spectrum of congruence hyperbolic manifolds. We prove Selberg type theorems on the first eigenvalue of the laplacian on differential forms. The method of proof is representation theoritic, we hope the different chapters may as well serve as an introduction to the modern theory of automorphic forms and its application to spectral questions. The second part of the book is of a more differential geometric flavor, a new kind of lifting of cohomology classes is proved.

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 This book is made of two parts. background 0.86 0.19 0.02 asserted 1.00
s1 The first is concerned with the differential form spectrum of congruence hyperbolic manifolds. contribution 0.61 0.17 0.05 asserted 0.99
s2 We prove Selberg type theorems on the first eigenvalue of the laplacian on differential forms. result 0.72 0.94 0.46 asserted 1.00
s3 The method of proof is representation theoritic, we hope the different chapters may as well serve as an introduction to the modern theory of automorphic forms and its application to spectral questions. method 0.92 0.38 0.07 hedged possibility 0.86
s4 The second part of the book is of a more differential geometric flavor, a new kind of lifting of cohomology classes is proved. contribution 0.71 0.91 0.14 asserted 1.00

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

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  • 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

This book is made of two parts. The first is concerned with the differential form spectrum of congruence hyperbolic manifolds. We prove Selberg type theorems on the first eigenvalue of the laplacian on differential forms. The method of proof is representation theoritic, we hope the different chapters may as well serve as an introduction to the modern theory of automorphic forms and its application to spectral questions. The second part of the book is of a more differential geometric flavor, a new kind of lifting of cohomology classes is proved.

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