{"paper":{"title":"Asymptotics for cuspidal representations by functoriality from GL(2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Huixue Lao, Mark McKee, Yangbo Ye","submitted_at":"2015-10-05T16:21:59Z","abstract_excerpt":"Let $\\pi$ be a unitary automorphic cuspidal representation of $GL_2(\\mathbb{Q}_\\mathbb{A})$ with Fourier coefficients $\\lambda_\\pi(n)$. Asymptotic expansions of certain sums of $\\lambda_\\pi(n)$ are proved using known functorial liftings from $GL_2$, including symmetric powers, isobaric sums, exterior square from $GL_4$ and base change. These asymptotic expansions are manifestation of the underlying functoriality and reflect value distribution of $\\lambda_\\pi(n)$ on integers, squares, cubes and fourth powers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01208","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"}