{"paper":{"title":"Converse Theorem Meets Gauss Sums (with an appendix by Zhiwei Yun)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Chufeng Nien, Lei Zhang","submitted_at":"2018-06-13T05:29:22Z","abstract_excerpt":"This paper verifies $n\\times 1$ Local Converse Theorem for twisted gamma factors of irreducible cuspidal representations of ${\\rm GL}_n({\\mathbb F}_p)$, for $n\\leq 5,$ and of irreducible generic representations, for $n<\\frac{q-1}{2\\sqrt{q}}+1$ in the appendix by Zhiwei Yun, where $p$ is a prime and q is a power of $p$. The counterpart of $n\\times 1$ converse theorem for level zero cuspidal representations also follows the established relation between gamma factors of ${\\rm GL}_n({\\mathcal F})$ and that of ${\\rm GL}_n({\\mathbb F}_q)$, where ${\\mathcal F}$ denotes a $p$-adic field whose residue "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04850","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"}