{"paper":{"title":"Estimates of Hilbert modular cusp forms of half-integral and integral weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anilatmaja Aryasomayajula","submitted_at":"2015-10-10T13:31:35Z","abstract_excerpt":"Let $\\Gamma$ be a cocompact, discrete, and irreducible subgroup of $\\mathrm{PSL}_{2}(\\mathbb{R})^{n}$. Let $\\nu$ be a unitary character of $\\Gamma$. For $k\\in1\\slash 2\\,\\mathbb{Z}$, let $\\sknu$ denote the complex vector space of cusp forms of weight-$\\tk=\\k$ and nebentypus $\\nu^{2k}$ with respect to $\\Gamma$. We assume that $\\omega_{X,\\nu}$, the line bundle of cusp forms of weight-$\\tilde{1\\slash 2}:=(1\\slash 2,\\ldots,1\\slash2)$ with nebentypus $\\nu$ over $X$ exists. Let $\\lbrace f_{1},\\ldots,f_{j_{\\tk}} \\rbrace$ denote an orthonormal basis of $\\sknu$. In this article, we show that as $k\\right"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02925","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"}