Edge Zeta Functions and Eigenvalues for Buildings of Finite Groups of Lie Type

[2405.14395] Edge Zeta Functions and Eigenvalues for Buildings of Finite Groups of Lie Type Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Combinatorics arXiv:2405.14395 (math) [Submitted on 23 May 2024 ( v1 ), last revised 15 Apr 2026 (this version, v3)] Title: Edge Zeta Functions and Eigenvalues for Buildings of Finite Groups of Lie Type Authors: Jianhao Shen View a PDF of the paper titled Edge Zeta Functions and Eigenvalues for Buildings of Finite Groups of Lie Type, by Jianhao Shen View PDF HTML (experimental) Abstract: For the Tits building B(G) of a finite group of Lie type G(Fq), we study the edge zeta function, which enumerates edge-geodesic cycles in the 1-skeleton. We show that every nonzero edge eigenvalue becomes a power of q after raising to a bounded exponent k depending on the type of G. The proof is uniform across types using a Hecke algebra approach. This extends previous results for type A and for oppositeness graphs to the full edge-geodesic setting and all finite groups of Lie type. Subjects: Combinatorics (math.CO) ; Number Theory (math.NT); Representation Theory (math.RT) Cite as: arXiv:2405.14395 [math.CO] (or arXiv:2405.14395v3 [math.CO] for this version) https://doi.org/10.48550/arXiv.2405.14395 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jianhao Shen [ view email ] [v1] Thu, 23 May 2024 10:12:31 UTC (16 KB) [v2] Mon, 13 Oct 2025 19:16:14 UTC (47 KB) [v3] Wed, 15 Apr 2026 09:02:14 UTC (48 KB) Full-text links: Access Paper: View a PDF of the paper titled Edge Zeta Functions and Eigenvalues for Buildings of Finite Groups of Lie Type, by Jianhao Shen View PDF HTML (experimental) TeX Source view license Current browse context: math.CO < prev | next > new | recent | 2024-05 Change to browse by: math math.NT math.RT 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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