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A particular case of our conjecture states that if $f := \\sum_{n \\geq 0} a(n)x^n$ and $g := \\sum_{n \\geq 0} b(n)x^n$ represent, respectively, an algebraic and a rational function over a global field $K$ such that $b(n) \\neq 0$ for all $n$ and the coefficients of the power series $h := \\sum_{n \\geq 0} a(n)/b(n)x^n$ are contained in a finitely generated ring, then $h$ is algebraic. We prove this conjecture if either (i) $g$ has a simple pole of a strictly maximal absolute value at some place; or (ii)"},"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":"1309.1920","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-08T01:33:09Z","cross_cats_sorted":[],"title_canon_sha256":"4e115acfd0e851af7069a8ccfd2e894aab184be0b27217c65964b1aad2ee7562","abstract_canon_sha256":"6fe02ceba778e41b2385b1ba4e3aa03b294464f4e6b5948262b44c39d0a069b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:57.029987Z","signature_b64":"6BPNYP/DMsEJ8//OJEV27uhotqStQBfloipPZYKNsc9YO00oeXKnHrSYo0wUdHNVAwdHaHl5omMJf/Hv9k/9Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4724682566deed55b02363fa59454933445de4cc55c1732350ca75a1bdea64c8","last_reissued_at":"2026-05-18T03:13:57.029368Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:57.029368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on a generalization of the Hadamard quotient theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Vesselin Dimitrov","submitted_at":"2013-09-08T01:33:09Z","abstract_excerpt":"We consider a generalization of the \"Hadamard quotient theorem\" of Pourchet and van der Poorten. 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