The sum of Lagrange numbers
Combining McShane’s identity on a hyperbolic punctured torus with well-known geometric interpretations of the Markov Uniqueness Conjecture (MUC), we find that MUC is equivalent to the identity ∑n=1∞(3−Ln)=4−φ−2, where Ln is the nth Lagrange number and φ=1+52 is the golden ratio.
Gespeichert in:
| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
August 20, 2021
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| In: |
Proceedings of the American Mathematical Society
Year: 2021, Jahrgang: 149, Heft: 12, Pages: 5385-5391 |
| ISSN: | 1088-6826 |
| DOI: | 10.1090/proc/15527 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1090/proc/15527 Verlag, lizenzpflichtig, Volltext: https://www.ams.org/proc/2021-149-12/S0002-9939-2021-15527-5/ 
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| Verfasserangaben: | Jonah Gaster and Brice Loustau ; (communicated by David Futer) |
MARC
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| 520 | |a Combining McShane’s identity on a hyperbolic punctured torus with well-known geometric interpretations of the Markov Uniqueness Conjecture (MUC), we find that MUC is equivalent to the identity ∑n=1∞(3−Ln)=4−φ−2, where Ln is the nth Lagrange number and φ=1+52 is the golden ratio. | ||
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