{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:V726GIB7QWC5HU752T54NFS6L5","short_pith_number":"pith:V726GIB7","schema_version":"1.0","canonical_sha256":"aff5e3203f8585d3d3fdd4fbc6965e5f7e1d7c1a773ecb8e47ed2c0c783ba02d","source":{"kind":"arxiv","id":"1207.6939","version":1},"attestation_state":"computed","paper":{"title":"On the Odlyzko-Stanley enumeration problem and Waring's problem over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Jiyou Li","submitted_at":"2012-07-30T13:50:40Z","abstract_excerpt":"We obtain an asymptotic formula on the Odlyzko-Stanley enumeration problem.\nLet $N_m^*(k,b)$ be the number of $k$-subsets\n$S\\subseteq F_p^*$ such that $\\sum_{x\\in S}x^m=b$.\nIf $m<p^{1-\\delta}$, then there is a constant\n$\\epsilon=\\epsilon(\\delta)>0$ such that\n| N_m^*(k,b)-p^{-1}{p-1 \\choose k}|\\leq {p^{1-\\epsilon}+mk-m \\choose k}.\n  In addition, let $\\gamma'(m,p)$ denote the distinct Waring's number $(\\mod p)$, the smallest positive integer $k$ such that every integer is a sum of m-th powers of $k$-distinct elements $(\\mod p)$. The above bound implies that there is a constant $\\epsilon(\\delta)>"},"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":"1207.6939","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-30T13:50:40Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1a45702e097b93e5e0755b4ac9ac164ea5b6fbe2482f0e40f55d0e5ac8f8c754","abstract_canon_sha256":"ae2b73369c2623eba26bd4abb7990478fbfeb913eb737d0b51cb248f87b25047"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:48.193854Z","signature_b64":"cfJyJ6/I8xJYjtOZtCAGU6ddUpsNl55ehvvxosI3o1fvkNQSMwa1AnAULk6za1heJwlRyHhJxsY2lF/fYUsPDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aff5e3203f8585d3d3fdd4fbc6965e5f7e1d7c1a773ecb8e47ed2c0c783ba02d","last_reissued_at":"2026-05-18T03:49:48.192971Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:48.192971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Odlyzko-Stanley enumeration problem and Waring's problem over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Jiyou Li","submitted_at":"2012-07-30T13:50:40Z","abstract_excerpt":"We obtain an asymptotic formula on the Odlyzko-Stanley enumeration problem.\nLet $N_m^*(k,b)$ be the number of $k$-subsets\n$S\\subseteq F_p^*$ such that $\\sum_{x\\in S}x^m=b$.\nIf $m<p^{1-\\delta}$, then there is a constant\n$\\epsilon=\\epsilon(\\delta)>0$ such that\n| N_m^*(k,b)-p^{-1}{p-1 \\choose k}|\\leq {p^{1-\\epsilon}+mk-m \\choose k}.\n  In addition, let $\\gamma'(m,p)$ denote the distinct Waring's number $(\\mod p)$, the smallest positive integer $k$ such that every integer is a sum of m-th powers of $k$-distinct elements $(\\mod p)$. 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