Finite and Symmetric Multiple $T$-Values

[2608.27541] Finite and Symmetric Multiple $T$-Values Skip to main content Search Submit Donate Log in Mathematics > Number Theory arXiv:2608.27541 (math) [Submitted on 27 Aug 2026] Title: Finite and Symmetric Multiple $T$-Values Authors: Aaron Cheng , Jianqiang Zhao View PDF HTML (experimental) Abstract: The multiple $T$-values (MTVs), first studied by Kaneko and Tsumura, are a variation of the multiple zeta values (MZVs) with restricted product structure. Motivated by a deep conjecture of Kaneko and Zagier relating finite MZVs and symmetric MZVs, which was extended to Euler sums by Zhao, we study finite and symmetric multiple $T$-values. In particular, we show that finite MTVs satisfy Hoffman-type duality relations at low height, confirming several conjectures of the second author and discovering new families of identities. In proving relations among symmetric MTVs, our work builds on Xu and Zhao's theory of multiple mixed values, the relations of double zeta values discovered by Gangl, Kaneko and Zagier, and the (weighted) sum formulas of double Euler sums discovered by Berger et al. We then use generating functions derived from the integral structure of MTVs to establish the corresponding relations for finite MTVs. These results aid in the computation of dimensions of the $\Q$-vector space spanned by finite and symmetric MTVs (modulo $\zeta(2)$ products), providing strong evidence for an isomorphism between the two spaces. Comments: 23 pages Subjects: Number Theory (math.NT) MSC classes: 11M32, 11B68, 68W30 Cite as: arXiv:2608.27541 [math.NT] (or arXiv:2608.27541v1 [math.NT] for this version) https://doi.org/10.48550/arXiv.2608.27541 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jianqiang Zhao [ view email ] [v1] Thu, 27 Aug 2026 16:16:07 UTC (20 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.NT < prev | next > new | recent | 2026-08 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation 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)

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