{"paper":{"title":"Density of Self-Dual Automorphic Representations of GL_n(A_Q)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Vitezslav Kala","submitted_at":"2014-06-02T14:38:42Z","abstract_excerpt":"We study the number $N_{\\mathrm{sd}}^K(\\lambda)$ of self-dual cuspidal automorphic representations of $GL_N(\\mathbb{A_Q})$ which are $K$-spherical with respect to a fixed compact subgroup $K$ and whose Laplacian eigenvalue is $\\leq \\lambda$. We prove Weak Weyl's Law for $N_{\\mathrm{sd}}^K(\\lambda)$ in the form that there are positive constants $c_1, c_2$ (depending on $K$) and $d$ such that $c_1\\lambda^{d/2}\\leq N_{\\mathrm{sd}}^K(\\lambda)\\leq c_2\\lambda^{d/2}$ for all sufficiently large $\\lambda$. When $N=2n$ is even and $K$ is a maximal compact subgroup at all places, we prove Weyl's Law for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0385","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"}