Spectral Theory of Isogeny Graphs

[2308.13913] Spectral Theory of Isogeny Graphs Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Number Theory arXiv:2308.13913 (math) [Submitted on 26 Aug 2023 ( v1 ), last revised 7 Apr 2026 (this version, v5)] Title: Spectral Theory of Isogeny Graphs Authors: Giulio Codogni , Guido Maria Lido View a PDF of the paper titled Spectral Theory of Isogeny Graphs, by Giulio Codogni and Guido Maria Lido View PDF HTML (experimental) Abstract: We consider finite graphs whose vertexes are supersingular elliptic curves, possibly with level structure, and edges are isogenies. They can be applied to the study of modular forms and to isogeny based cryptography. The main result of this paper is an upper bound on the modules of the eigenvalues of their adjacency matrices, which in particular implies that these graphs are Ramanujan. We also study the asymptotic distribution of the eigenvalues of the adjacency matrices, the number of connected components, the automorphisms of the graphs, and the connection between the graphs and modular forms. Comments: Accepted for publication on the Journal of Number Theory. Exposition improved Subjects: Number Theory (math.NT) ; Algebraic Geometry (math.AG) MSC classes: 14K02, 14H52, 11F52, 05C48, 14G50 Cite as: arXiv:2308.13913 [math.NT] (or arXiv:2308.13913v5 [math.NT] for this version) https://doi.org/10.48550/arXiv.2308.13913 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Journal of Number Theory, Volume 286, September 2026, Pages 131-184 Related DOI : https://doi.org/10.1016/j.jnt.2026.02.006 Focus to learn more DOI(s) linking to related resources Submission history From: Giulio Codogni [ view email ] [v1] Sat, 26 Aug 2023 16:30:32 UTC (41 KB) [v2] Fri, 12 Apr 2024 10:06:53 UTC (205 KB) [v3] Thu, 4 Jul 2024 15:20:39 UTC (368 KB) [v4] Fri, 9 May 2025 14:35:30 UTC (374 KB) [v5] Tue, 7 Apr 2026 09:41:03 UTC (376 KB) Full-text links: Access Paper: View a PDF of the paper titled Spectral Theory of Isogeny Graphs, by Giulio Codogni and Guido Maria Lido View PDF HTML (experimental) TeX Source view license Current browse context: math.NT < prev | next > new | recent | 2023-08 Change to browse by: math math.AG References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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