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We use these results and methods to derive non-trivial upper bounds for the number of hyperelliptic curves $Y^2=X^{2g+1} + a_{2g-1}X^{2g-1} +...+ a_1X+a_0$ over the finite field $\\F_p$ of $p$ elements, with coefficients in a $2g$-dimensional cube $ (a_0,..., a_{2g-1})\\in [R_0+1,R_0+M]\\times...\\times [R_{2g-1}+1,R_{2g-1}+M]$ that are is"},"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":"1111.1543","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-07T11:13:31Z","cross_cats_sorted":[],"title_canon_sha256":"88cbfc7b6aa2f49f53c9b901339fed5203343aa21a477dc2033816c194a18372","abstract_canon_sha256":"597c073cf1f1e111aa067b1146be64ee4e2139cb85f4e7f8bced984a9a86e301"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:13.669136Z","signature_b64":"sOhvG+sllxY+zknlPPaN7Y4BIIN2UV00PGScMKuii1QNWOJMjrzipKyFaJBwbNpoG6b7RdmzOz2/pkuQIxD9Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b2950b747b0f8f59b4a3469f3304fc940bcb0939decd448b2eef7705bee9d0b","last_reissued_at":"2026-05-18T03:59:13.668362Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:13.668362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Points on curves in small boxes en applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ana Zumalac\\'arregui, Igor E. 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