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We give a method based on explicit extensions for constructing towers of function fields over F_q with finitely many prescribed invariants being positive, and towers of function fields over F_q, for q a square, wi"},"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":"1111.5600","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-23T19:54:58Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c09363f80a5b8f0add13b181d93804beacbc3d3a3f41deb19cd608085c5bc4fa","abstract_canon_sha256":"a24b7193757261a834f76f954d29650a9b49268ec9932cfcf296dd5568b6cce3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:25.304887Z","signature_b64":"GJqvDYhLorR2YNAzUjL5F5Z40iwDEjGQfb+jc1kNntMYzfvNjSiAf7ow1xYu+XcGGzfeRhghKrT84aMtqhhlAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9180181b19cd7d174bf3889b64c0a17166db4f6e8611d09ca4e8aa29eefc25b6","last_reissued_at":"2026-05-18T03:36:25.304477Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:25.304477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Invariants of Towers of Function Fields over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Florian Hess, Henning Stichtenoth, Seher Tutdere","submitted_at":"2011-11-23T19:54:58Z","abstract_excerpt":"We consider a tower of function fields F=(F_n)_{n\\geq 0} over a finite field F_q and a finite extension E/F_0 such that the sequence \\mathcal{E):=(EF_n)_{n\\goq 0} is a tower over the field F_q. 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