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Let $t=x^{m(q-1)}$ and $H=\\mathbb{K}(t)$. The extension $F|H$ is a non-Galois extension. Let $K$ be the Galois closure of $F$ with respect to $H$. By a result of Stichtenoth, $K$ has genus $g(K)=(qm-1)(q-1)$, $p$-rank (Hasse-Witt invariant) $\\gamma(K)=(q-1)^2$ and a $\\mathbb{K}$-automorphism group of order at least $2q^2m(q-1)$. In this paper we prove t"},"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":"1701.02186","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-09T14:15:30Z","cross_cats_sorted":[],"title_canon_sha256":"9127fc90ec33c2a4eab4151adb39e29d37d275768db1a7d0bfacd2394b8604dd","abstract_canon_sha256":"ce67d195500711119785dad8da79c9412a270127272b06d4ae1ccdb31de851b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:11.493051Z","signature_b64":"VFzvb3MO2K70afLm70yDIgVS0qtto9t3OpQAbhEQn5hcr+Bvm8QeDXM3rrLa0CiU6tajR2ui1xDd6rdyepqyBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31f28944a147aca0cb9208993358f8317d65947db25cd00f1022ea8e3c19b5d3","last_reissued_at":"2026-05-18T00:53:11.492612Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:11.492612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transcendency Degree One Function Fields Over a Finite Field with Many Automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"G\\'abor Korchm\\'aros, Maria Montanucci, Pietro Speziali","submitted_at":"2017-01-09T14:15:30Z","abstract_excerpt":"Let $\\mathbb{K}$ be the algebraic closure of a finite field $\\mathbb{F}_q$ of odd characteristic $p$. For a positive integer $m$ prime to $p$, let $F=\\mathbb{K}(x,y)$ be the transcendency degree $1$ function field defined by $y^q+y=x^m+x^{-m}$. Let $t=x^{m(q-1)}$ and $H=\\mathbb{K}(t)$. The extension $F|H$ is a non-Galois extension. Let $K$ be the Galois closure of $F$ with respect to $H$. By a result of Stichtenoth, $K$ has genus $g(K)=(qm-1)(q-1)$, $p$-rank (Hasse-Witt invariant) $\\gamma(K)=(q-1)^2$ and a $\\mathbb{K}$-automorphism group of order at least $2q^2m(q-1)$. 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