{"paper":{"title":"Special values of Kloosterman sums and binomial bent functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chunming Tang, Yanfeng Qi","submitted_at":"2013-12-27T04:44:38Z","abstract_excerpt":"Let $p\\ge 7$, $q=p^m$. $K_q(a)=\\sum_{x\\in \\mathbb{F}_{p^m}} \\zeta^{\\mathrm{Tr}^m_1(x^{p^m-2}+ax)}$ is the Kloosterman sum of $a$ on $\\mathbb{F}_{p^m}$, where $\\zeta=e^{\\frac{2\\pi\\sqrt{-1}}{p}}$. The value $1-\\frac{2}{\\zeta+\\zeta^{-1}}$ of $K_q(a)$ and its conjugate have close relationship with a class of binomial function with Dillon exponent. This paper first presents some necessary conditions for $a$ such that $K_q(a)=1-\\frac{2}{\\zeta+\\zeta^{-1}}$. Further, we prove that if $p=11$, for any $a$, $K_q(a)\\neq 1-\\frac{2}{\\zeta+\\zeta^{-1}}$. And for $p\\ge 13$, if $a\\in \\mathbb{F}_{p^s}$ and $s=\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7191","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"}