{"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/drinfeld-modular-polynomials-of-level-t","title":"Drinfeld modular polynomials of level $T$","arxiv_id":"2412.11324","date":"2024-12-15","proceeding":null,"authors":["Florian Breuer","Mahefason Heriniaina Razafinjatovo"],"abstract":"We investigate Drinfeld modular polynomials parametrizing $T$-isogenies between Drinfeld $\\mathbb{F}_q[T]$-modules of rank $r\\geq 2$. By providing an explicit classification of such isogenies, we derive explicit bounds on the $T$-degrees of the coefficients of the associated modular polynomials. In particular, we obtain exact expressions for the height (i.e. degree of the largest coefficient) of these modular polynomials. Numerical computations show that the bounds on the smaller coefficients are often sharp, too.","url_abs":"https://arxiv.org/abs/2412.11324v2","url_pdf":"https://arxiv.org/pdf/2412.11324v2.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":"drinfeld-modular-polynomials-of-level-t","repo_url":"https://github.com/florianbreuer/drinfeldmodularpolynomialslevelt","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}