{"paper":{"title":"Explicit equations for Drinfeld modular towers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alp Bassa, Peter Beelen","submitted_at":"2011-10-27T13:23:14Z","abstract_excerpt":"Elaborating on ideas of Elkies, we show how recursive equations for towers of Drinfeld modular curves $(X_0(P^n))_{n\\ge 0}$ for $P\\in \\mathbb F_q[T]$ can be read of directly from the modular polynomial $\\Phi_P(X,Y)$ and how this naturally leads to recursions of depth two. Although the modular polynomial $\\Phi_T(X,Y)$ is not known in general, using generators and relations given by Schweizer, we find unreduced recursive equations over $\\mathbb F_q(T)$ for the tower $(X_0(T^n))_{n\\ge 2}$ and of a small variation of it (its partial Galois closure). Reducing at various primes, one obtains towers o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6076","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}