{"paper":{"title":"A Mild Tchebotarev Theorem for GL$(n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dinakar Ramakrishnan","submitted_at":"2010-03-23T19:41:17Z","abstract_excerpt":"It is well known that the Tchebotarev density theorem implies that an irreducible $\\ell$-adic representation $\\rho$ of the absolute Galois group of a number field $K$ is determined (up to isomorphism) by the characteristic polynomials of Frobenius elements at any set of primes of density 1. In this Note we make some progress on the automorphic side for GL$(n)$ by showing that, given a cyclic extension $K/k$ of number fields of prime degree $p$, a cuspidal automorphic representation $\\pi$ of GL$(n,{\\mathbb A}_K)$ is determined up to twist equivalence by the knowledge of its local components at "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4498","kind":"arxiv","version":3},"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"}