{"paper":{"title":"Gauss sums of some matrix groups over $\\Bbb Z/n\\Bbb Z$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Guoxing He, Su Hu, Yan Li, Yingtong Meng","submitted_at":"2018-05-24T15:27:14Z","abstract_excerpt":"In this paper, we will explicitly calculate Gauss sums for the general linear groups and the special linear groups over $\\Bbb Z_n$, where $\\Bbb Z_n=\\Bbb Z/n \\Bbb Z$ and $n>0$ is an integer. For $r$ being a positive integer, the formulae of Gauss sums for ${\\rm GL}_r(\\Bbb Z_n)$ can be expressed in terms of classical Gauss sums over $\\Bbb Z_n$, while the formulae of Gauss sums for ${\\rm SL}_r(\\Bbb Z_n)$ can be expressed in terms of hyper-Kloosterman sums over $\\Bbb Z_n$. As an application, we count the number of $r\\times r$ invertible matrices over $\\Bbb Z_n$ with given trace by using the the fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09729","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"}