{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:6OXO6K53634FFIDDKBKHGJKBKY","short_pith_number":"pith:6OXO6K53","schema_version":"1.0","canonical_sha256":"f3aeef2bbbf6f852a0635054732541563b3ac3601a2b2f4fa1f1c782e0ebdcaf","source":{"kind":"arxiv","id":"1811.07244","version":1},"attestation_state":"computed","paper":{"title":"Proceedings Paper for REU Project Involving Counting Eta-Quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Allison Arnold-Roksandich, Kevin James, Rodney Keaton","submitted_at":"2018-11-17T23:19:31Z","abstract_excerpt":"It is known that all modular forms on $SL_2(Z)$ can be expressed as a rational function in $\\eta(z)$, $\\eta(2z)$ and $\\eta(4z)$. By using a theorem by Gordon, Hughes, and Newman, and calculating the order of vanishing, we can compute the $\\eta$-quotients for a given level. Using this count, knowing how many $\\eta$-quotients are linearly independent and using the dimension formula, we can figure out how the $\\eta$-quotients span higher levels. In this paper, we primarily focus on the case where $N=p$ a prime, and some discussion for non-prime indicies."},"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":"1811.07244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-17T23:19:31Z","cross_cats_sorted":[],"title_canon_sha256":"e1dd519ee214f6d1fb3cfa19b548c106b863d1166892e58e5c1ee64fdc603f6c","abstract_canon_sha256":"85a0ba7ca7b812438c9871e4d79a734c52893d51b046b694ed4e6e993795875d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:28.515833Z","signature_b64":"gCRFe/klyPIX/kDsUIAf0xd7scDZrhb5EVIm20NFSSqwmssn0PZJe4mNr2iYjdxRjlmrTqS2tS7BTDJU89wdDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3aeef2bbbf6f852a0635054732541563b3ac3601a2b2f4fa1f1c782e0ebdcaf","last_reissued_at":"2026-05-18T00:00:28.515190Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:28.515190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proceedings Paper for REU Project Involving Counting Eta-Quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Allison Arnold-Roksandich, Kevin James, Rodney Keaton","submitted_at":"2018-11-17T23:19:31Z","abstract_excerpt":"It is known that all modular forms on $SL_2(Z)$ can be expressed as a rational function in $\\eta(z)$, $\\eta(2z)$ and $\\eta(4z)$. By using a theorem by Gordon, Hughes, and Newman, and calculating the order of vanishing, we can compute the $\\eta$-quotients for a given level. Using this count, knowing how many $\\eta$-quotients are linearly independent and using the dimension formula, we can figure out how the $\\eta$-quotients span higher levels. In this paper, we primarily focus on the case where $N=p$ a prime, and some discussion for non-prime indicies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07244","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":"1811.07244","created_at":"2026-05-18T00:00:28.515279+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.07244v1","created_at":"2026-05-18T00:00:28.515279+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.07244","created_at":"2026-05-18T00:00:28.515279+00:00"},{"alias_kind":"pith_short_12","alias_value":"6OXO6K53634F","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_16","alias_value":"6OXO6K53634FFIDD","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_8","alias_value":"6OXO6K53","created_at":"2026-05-18T12:32:11.075285+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/6OXO6K53634FFIDDKBKHGJKBKY","json":"https://pith.science/pith/6OXO6K53634FFIDDKBKHGJKBKY.json","graph_json":"https://pith.science/api/pith-number/6OXO6K53634FFIDDKBKHGJKBKY/graph.json","events_json":"https://pith.science/api/pith-number/6OXO6K53634FFIDDKBKHGJKBKY/events.json","paper":"https://pith.science/paper/6OXO6K53"},"agent_actions":{"view_html":"https://pith.science/pith/6OXO6K53634FFIDDKBKHGJKBKY","download_json":"https://pith.science/pith/6OXO6K53634FFIDDKBKHGJKBKY.json","view_paper":"https://pith.science/paper/6OXO6K53","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.07244&json=true","fetch_graph":"https://pith.science/api/pith-number/6OXO6K53634FFIDDKBKHGJKBKY/graph.json","fetch_events":"https://pith.science/api/pith-number/6OXO6K53634FFIDDKBKHGJKBKY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6OXO6K53634FFIDDKBKHGJKBKY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6OXO6K53634FFIDDKBKHGJKBKY/action/storage_attestation","attest_author":"https://pith.science/pith/6OXO6K53634FFIDDKBKHGJKBKY/action/author_attestation","sign_citation":"https://pith.science/pith/6OXO6K53634FFIDDKBKHGJKBKY/action/citation_signature","submit_replication":"https://pith.science/pith/6OXO6K53634FFIDDKBKHGJKBKY/action/replication_record"}},"created_at":"2026-05-18T00:00:28.515279+00:00","updated_at":"2026-05-18T00:00:28.515279+00:00"}