{"paper":{"title":"Inducing Whittaker Functions from Higher Ranks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Vishal Muthuvel","submitted_at":"2026-05-28T04:29:07Z","abstract_excerpt":"We construct a family of Whittaker functions for $SL(m,\\mathbb{Z})$ induced directly from Whittaker functions for $SL(n,\\mathbb{Z})$, for any $2 \\leq m<n$. Given Jacquet's Whittaker function $W_{\\alpha,N}^{(n)}$ on the generalized upper half-plane $\\mathfrak{h}^n$, we show that the function $V_{\\alpha,N}^{(m)}:\\mathfrak{h}^m\\to\\mathbb{C}$ defined by restricting $W_{\\alpha,N}^{(n)}$ to the block-diagonal embedding $\\mathfrak{h}^m\\hookrightarrow\\mathfrak{h}^n$ is a Whittaker function for $SL(m,\\mathbb{Z})$, provided the Langlands parameters $\\alpha=(\\alpha_i)_{1\\leq i\\leq n}$ satisfy $\\sum_{i=1}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29342","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.29342/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}