{"paper":{"title":"Schneider-Siegel theorem for a family of values of a harmonic weak Maass form at Hecke orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dohoon Choi, Subong Lim","submitted_at":"2018-12-05T01:17:54Z","abstract_excerpt":"Let $j(z)$ be the modular $j$-invariant function. Let $\\tau$ be an algebraic number in the complex upper half plane $\\mathbb{H}$. It was proved by Schneider and Siegel that if $\\tau$ is not a CM point, i.e., $[\\mathbb{Q}(\\tau):\\mathbb{Q}]\\neq2$, then $j(\\tau)$ is transcendental. Let $f$ be a harmonic weak Maass form of weight $0$ on $\\Gamma_0(N)$. In this paper, we consider an extension of the results of Schneider and Siegel to a family of values of $f$ on Hecke orbits of $\\tau$.\n  For a positive integer $m$, let $T_m$ denote the $m$-th Hecke operator. Suppose that the coefficients of the prin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01770","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"}