{"paper":{"title":"Complete Solving for Explicit Evaluation of Gauss Sums in the Index 2 Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jing Yang, Lingli Xia","submitted_at":"2009-11-29T09:41:05Z","abstract_excerpt":"Let $p$ be a prime number, $q=p^f$ for some positive integer $f$, $N$ be a positive integer such that $\\gcd(N,p)=1$, and let $\\k$ be a primitive multiplicative character of order $N$ over finite field $\\fq$. This paper studies the problem of explicit evaluation of Gauss sums in \"\\textsl{index 2 case}\" (i.e. $f=\\f{\\p(N)}{2}=[\\zn:\\pp]$, where $\\p(\\cd)$ is Euler function). Firstly, the classification of the Gauss sums in index 2 case is presented. Then, the explicit evaluation of Gauss sums $G(\\k^\\la) (1\\laN-1)$ in index 2 case with order $N$ being general even integer (i.e. $N=2^{r}\\cd N_0$ wher"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.5472","kind":"arxiv","version":3},"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"}