{"paper":{"title":"Strong exponent bounds for the local Rankin-Selberg convolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Colin J Bushnell, Guy Henniart","submitted_at":"2016-03-03T16:15:11Z","abstract_excerpt":"Let $F$ be a non-Archimedean locally compact field. Let $\\sigma$ and $\\tau$ be finite-dimensional semisimple representations of the Weil-Deligne group of $F$. We give strong upper and lower bounds for the Artin and Swan exponents of $\\sigma\\otimes\\tau$ in terms of those of $\\sigma$ and $\\tau$. We give a different lower bound in terms of $\\sigma\\otimes\\check\\sigma$ and $\\tau\\otimes\\check\\tau$. Using the Langlands correspondence, we obtain the bounds for Rankin-Selberg exponents."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01152","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"}