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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1312.7191","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-12-27T04:44:38Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"8ee1b654dda2326fdd0764541a51ab118bbf4ccafd45bb7f46147f0b25c1d671","abstract_canon_sha256":"971605246e6c84da153806a9637b38ff65ffe9c30ea9b47965633930420fa61d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:45.546002Z","signature_b64":"znJ5AkLkRB6tUddtN11dWiZpjjMa/EGzi0XJ3h5RGeerTbOxEJBva7Xwyg5QVjTluvrFrm+KtmqGikEVDW0FCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9aaa03ef42e82684aa2d682e266ef377ac78692d20aeafd8b34b9717866a5e24","last_reissued_at":"2026-05-18T03:03:45.545423Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:45.545423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $a$, $K_q(a)\\neq 1-\\frac{2}{\\zeta+\\zeta^{-1}}$. 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