{"paper":{"title":"Geometric Realization of Whittaker Functions and the Langlands Conjecture","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"D. Gaitsgory, D. Kazhdan, E. Frenkel, K. Vilonen","submitted_at":"1997-03-18T22:16:39Z","abstract_excerpt":"We prove the equivalence of two conjectural constructions of unramified cuspidal automorphic functions on the adelic group GL_n(A) associated to an irreducible l-adic local system of rank n on an algebraic curve X over a finite field. The existence of such a function is predicted by the Langlands conjecture.\n  The first construction, which was proposed by Shalika and Piatetski-Shapiro following Weil and Jacquet-Langlands (n=2), is based on considering the Whittaker function. The second construction, which was proposed recently by Laumon following Drinfeld (n=2) and Deligne (n=1), is geometric:"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9703022","kind":"arxiv","version":2},"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"}