{"paper":{"title":"On the zeros of a class of modular functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Katharine Woo, Naomi Sweeting","submitted_at":"2018-07-11T18:17:44Z","abstract_excerpt":"We generalize a number of works on the zeros of certain level 1 modular forms to a class of weakly holomorphic modular functions whose $q$-expansions satisfy \\[ f_k(A, \\tau) \\colon = q^{-k}(1+a(1)q+a(2)q^2+...) + O(q),\\] where $a(n)$ are numbers satisfying a certain analytic condition. We show that the zeros of such $f_k(\\tau)$ in the fundamental domain of $SL_2(\\mathbb{Z})$ lie on $|\\tau|=1$ and are transcendental. We recover as a special case earlier work of Witten on extremal \"partition\" functions $Z_k(\\tau)$. These functions were originally conceived as possible generalizations of construc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04310","kind":"arxiv","version":2},"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"}