{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/the-sum-of-lagrange-numbers","title":"The sum of Lagrange numbers","arxiv_id":"2008.07659","date":"2020-08-17","proceeding":null,"authors":["Jonah Gaster","Brice Loustau"],"abstract":"Combining McShane's identity on a hyperbolic punctured torus with Schmutz's work on the Markov Uniqueness Conjecture (MUC), we find that MUC is equivalent to the identity \\begin{equation} \\sum_{n=1}^\\infty \\, \\left( 3- L_n \\right) \\, = \\, 4 - \\varphi - \\sqrt 2 \\end{equation} where $L_n$ is the $n$th Lagrange number and $\\varphi=\\frac{1+\\sqrt5}2$ is the golden ratio.","url_abs":"http://arxiv.org/abs/2008.07659v1","url_pdf":"http://arxiv.org/pdf/2008.07659v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"the-sum-of-lagrange-numbers","repo_url":"https://github.com/seub/LagrangeSeries","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}