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.
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
August 20, 2021
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| In: |
Proceedings of the American Mathematical Society
Year: 2021, Volume: 149, Issue: 12, Pages: 5385-5391 |
| ISSN: | 1088-6826 |
| DOI: | 10.1090/proc/15527 |
| Online Access: | 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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| Author Notes: | Jonah Gaster and Brice Loustau ; (communicated by David Futer) |
| Summary: | 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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| Item Description: | Gesehen am 21.02.2022 |
| Physical Description: | Online Resource |
| ISSN: | 1088-6826 |
| DOI: | 10.1090/proc/15527 |