Drinfeld modular forms of higher rank from a lattice-oriented point of view

[2608.28014] Drinfeld modular forms of higher rank from a lattice-oriented point of view Skip to main content Search Submit Donate Log in Mathematics > Number Theory arXiv:2608.28014 (math) [Submitted on 28 Aug 2026] Title: Drinfeld modular forms of higher rank from a lattice-oriented point of view Authors: Liam Baker View PDF Abstract: A space $\mathcal{L}_N^r$ of Drinfeld modules of rank $r \geq 1$ with level structure, or equivalently lattices of rank $r$ with level structure, is introduced, and its irreducible components and group actions on it are investigated. A metric is defined on this space, its completion $\overleftarrow{\mathcal{L}_{N}^{r}}$ is established and the aforementioned group actions are extended to the completion. A decomposition of the completion into multiple smaller spaces $\mathcal{L}_N^s$ is proven. Drinfeld modular forms are defined as homogeneous holomorphic functions on $\mathcal{L}_{N}^{r}$ which are continuous on the completion $\overleftarrow{\mathcal{L}_{N}^{r}}$, and the group actions above are extended to actions on the spaces of modular forms. Finally, the modular forms defined here are compared with those of Basson, Breuer, and Pink and with those of Gekeler, and it is shown that the cusp forms (those which are zero on the boundary) coincide. Comments: 46 pages. To be published in Transactions of the AMS Subjects: Number Theory (math.NT) MSC classes: 11F52, 11G09, 11F23, 14G22 Cite as: arXiv:2608.28014 [math.NT] (or arXiv:2608.28014v1 [math.NT] for this version) https://doi.org/10.48550/arXiv.2608.28014 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Liam Baker [ view email ] [v1] Fri, 28 Aug 2026 07:30:56 UTC (70 KB) Full-text links: Access Paper: View PDF 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) Major funding support from (opens in new tab) (opens in new tab) (opens in new tab)

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