Abstract
It is a classical result of Dal’Bo that the length spectrum of a non-elementary Fuchsian group is nonarithmetic, namely, it generates a dense additive subgroup of R. In this note we provide an elementary proof of an extension of this theorem: a non-elementary Fuchsian group contains two elements whose lengths are linearly independent over Q, reproving a result of Prasad and Rapinchuk [9].
| Original language | English |
|---|---|
| Pages (from-to) | 825-828 |
| Number of pages | 4 |
| Journal | Comptes Rendus Mathematique |
| Volume | 363 |
| DOIs | |
| State | Published - 2025 |
Bibliographical note
Publisher Copyright:© 2025, Academie des sciences. All rights reserved.
Keywords
- Fuchsian group
- Length spectrum
- trace field
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