{"paper":{"title":"A comparison of automorphic and Artin L-series of GL(2)-type agreeing at degree one primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dinakar Ramakrishnan, Kimball Martin","submitted_at":"2015-02-14T06:52:14Z","abstract_excerpt":"Let $F/k$ be a cyclic extension of number fields of prime degree. Let $\\rho$ be an irreducible $2$-dimensional representation of Artin type of the absolute Galois group of $F$, and $\\pi$ a cuspidal automorphic representation of GL$_2(\\mathbb A_F)$, such that the $L$-functions $L(s,\\rho_v)$ and $L(s,\\pi_v)$ agree at all (but finitely many of) the places $v$ of degree one over $k$. We prove in this case that we have the global identity $L(s,\\rho)=L(s,\\pi)$, with $\\rho_v \\leftrightarrow \\pi_v$ being given by the local Langlands correspondence at all $v$. In particular, $\\pi$ is tempered and $L(s,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04175","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"}