{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:QTT67TELUDDUKHSCPAZBIFX42M","short_pith_number":"pith:QTT67TEL","schema_version":"1.0","canonical_sha256":"84e7efcc8ba0c7451e4278321416fcd32aee95e0f3bc4a5a7060c558841e9408","source":{"kind":"arxiv","id":"1701.09051","version":1},"attestation_state":"computed","paper":{"title":"Linear independence of values of G-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"St\\'ephane Fischler (LM-Orsay), Tanguy Rivoal (IF)","submitted_at":"2017-01-31T14:20:33Z","abstract_excerpt":"Given any non-polynomial $G$-function $F(z)=\\sum\\_{k=0}^\\infty A\\_k z^k$ of radius of convergence $R$, we consider the $G$-functions   $F\\_n^{[s]}(z)=\\sum\\_{k=0}^\\infty \\frac{A\\_k}{(k+n)^s}z^k$ for any integers $s\\geq 0$ and $n\\geq 1$. For any fixed algebraic number $\\alpha$ such that $0 \\textless{} \\vert  \\alpha \\vert \\textless{} R$ and any number field $\\mathbb{K}$ containing $\\alpha$ and the $A\\_k$'s, we define $\\Phi\\_{\\alpha, S}$ as the $\\mathbb{K}$-vector space generated by the values $F\\_n^{[s]}(\\alpha)$, $n\\ge 1$ and $0\\leq s\\leq S$. We prove that $u\\_{\\mathbb{K},F}\\log(S)\\leq \\dim\\_{\\m"},"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":"1701.09051","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-31T14:20:33Z","cross_cats_sorted":[],"title_canon_sha256":"d6921e1c5068697684ca5088a3fb55638e0502a847ebafa6daf1d2252351c8e4","abstract_canon_sha256":"d4c1158e294e8b368fee191668e6fb03496ee90eba00a23431dfb57eadb9662c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:38.557599Z","signature_b64":"LbHfW/dN2xmlItKTgpHlFAx0uyou5QrJPydlSt0U43yKGD0YINWsxSJJzFmFzeEqt7R1W0oPlVKa2Ju46NEkBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84e7efcc8ba0c7451e4278321416fcd32aee95e0f3bc4a5a7060c558841e9408","last_reissued_at":"2026-05-18T00:51:38.556979Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:38.556979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear independence of values of G-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"St\\'ephane Fischler (LM-Orsay), Tanguy Rivoal (IF)","submitted_at":"2017-01-31T14:20:33Z","abstract_excerpt":"Given any non-polynomial $G$-function $F(z)=\\sum\\_{k=0}^\\infty A\\_k z^k$ of radius of convergence $R$, we consider the $G$-functions   $F\\_n^{[s]}(z)=\\sum\\_{k=0}^\\infty \\frac{A\\_k}{(k+n)^s}z^k$ for any integers $s\\geq 0$ and $n\\geq 1$. For any fixed algebraic number $\\alpha$ such that $0 \\textless{} \\vert  \\alpha \\vert \\textless{} R$ and any number field $\\mathbb{K}$ containing $\\alpha$ and the $A\\_k$'s, we define $\\Phi\\_{\\alpha, S}$ as the $\\mathbb{K}$-vector space generated by the values $F\\_n^{[s]}(\\alpha)$, $n\\ge 1$ and $0\\leq s\\leq S$. We prove that $u\\_{\\mathbb{K},F}\\log(S)\\leq \\dim\\_{\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.09051","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1701.09051","created_at":"2026-05-18T00:51:38.557072+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.09051v1","created_at":"2026-05-18T00:51:38.557072+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.09051","created_at":"2026-05-18T00:51:38.557072+00:00"},{"alias_kind":"pith_short_12","alias_value":"QTT67TELUDDU","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_16","alias_value":"QTT67TELUDDUKHSC","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_8","alias_value":"QTT67TEL","created_at":"2026-05-18T12:31:39.905425+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QTT67TELUDDUKHSCPAZBIFX42M","json":"https://pith.science/pith/QTT67TELUDDUKHSCPAZBIFX42M.json","graph_json":"https://pith.science/api/pith-number/QTT67TELUDDUKHSCPAZBIFX42M/graph.json","events_json":"https://pith.science/api/pith-number/QTT67TELUDDUKHSCPAZBIFX42M/events.json","paper":"https://pith.science/paper/QTT67TEL"},"agent_actions":{"view_html":"https://pith.science/pith/QTT67TELUDDUKHSCPAZBIFX42M","download_json":"https://pith.science/pith/QTT67TELUDDUKHSCPAZBIFX42M.json","view_paper":"https://pith.science/paper/QTT67TEL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.09051&json=true","fetch_graph":"https://pith.science/api/pith-number/QTT67TELUDDUKHSCPAZBIFX42M/graph.json","fetch_events":"https://pith.science/api/pith-number/QTT67TELUDDUKHSCPAZBIFX42M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QTT67TELUDDUKHSCPAZBIFX42M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QTT67TELUDDUKHSCPAZBIFX42M/action/storage_attestation","attest_author":"https://pith.science/pith/QTT67TELUDDUKHSCPAZBIFX42M/action/author_attestation","sign_citation":"https://pith.science/pith/QTT67TELUDDUKHSCPAZBIFX42M/action/citation_signature","submit_replication":"https://pith.science/pith/QTT67TELUDDUKHSCPAZBIFX42M/action/replication_record"}},"created_at":"2026-05-18T00:51:38.557072+00:00","updated_at":"2026-05-18T00:51:38.557072+00:00"}