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We show that, for $n\\geq 5$, for $|q|\\leq 1-1/(\\alpha _0n)$ and for $k\\geq n$ there exists a unique zero $\\xi _k$ of $\\theta (q,.)$ satisfying the inequalities $|q|^{-k+1/2}<|\\xi _k|<|q|^{-k-1/2}$; all these zeros are simple ones. The moduli of the remaining $n-1$ zeros are $\\leq |q|^{-n+1/2}$. A {\\em spectral value} of $q$ is a value for which $\\theta (q,.)$ ha"},"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":"1704.01901","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-04-06T15:58:42Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"6de6171189f03722a9f92fe7db793dfbe7f327e918a295bf02a407184bc09dce","abstract_canon_sha256":"c8d2ada4fafaf25ae6c8d54f98b01d59a8d08328dd19541a5585883420c87f78"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:42.137954Z","signature_b64":"5tX6ptufpQj/DXzGORAYSac83PHHwsG1/Ow718T5N1Gc0x7Grf15ybXU934KosuDF8r7oYp9IaTpcrDAM71yDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffdfa7e3622fe8473a6249182ea32287f3f1dd266b04c8cd8089508da4499a20","last_reissued_at":"2026-05-17T23:46:42.137249Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:42.137249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A separation in modulus property of the zeros of a partial theta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"Vladimir Petrov Kostov","submitted_at":"2017-04-06T15:58:42Z","abstract_excerpt":"We consider the partial theta function $\\theta (q,z):=\\sum _{j=0}^{\\infty}q^{j(j+1)/2}z^j$, where $z\\in \\mathbb{C}$ is a variable and $q\\in \\mathbb{C}$, $0<|q|<1$, is a parameter. Set $\\alpha _0~:=~\\sqrt{3}/2\\pi ~=~0.2756644477\\ldots$. We show that, for $n\\geq 5$, for $|q|\\leq 1-1/(\\alpha _0n)$ and for $k\\geq n$ there exists a unique zero $\\xi _k$ of $\\theta (q,.)$ satisfying the inequalities $|q|^{-k+1/2}<|\\xi _k|<|q|^{-k-1/2}$; all these zeros are simple ones. The moduli of the remaining $n-1$ zeros are $\\leq |q|^{-n+1/2}$. A {\\em spectral value} of $q$ is a value for which $\\theta (q,.)$ ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01901","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":"1704.01901","created_at":"2026-05-17T23:46:42.137378+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.01901v1","created_at":"2026-05-17T23:46:42.137378+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01901","created_at":"2026-05-17T23:46:42.137378+00:00"},{"alias_kind":"pith_short_12","alias_value":"77P2PY3CF7UE","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"77P2PY3CF7UEOOTC","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"77P2PY3C","created_at":"2026-05-18T12:31:03.183658+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/77P2PY3CF7UEOOTCJEMC5IZCQ7","json":"https://pith.science/pith/77P2PY3CF7UEOOTCJEMC5IZCQ7.json","graph_json":"https://pith.science/api/pith-number/77P2PY3CF7UEOOTCJEMC5IZCQ7/graph.json","events_json":"https://pith.science/api/pith-number/77P2PY3CF7UEOOTCJEMC5IZCQ7/events.json","paper":"https://pith.science/paper/77P2PY3C"},"agent_actions":{"view_html":"https://pith.science/pith/77P2PY3CF7UEOOTCJEMC5IZCQ7","download_json":"https://pith.science/pith/77P2PY3CF7UEOOTCJEMC5IZCQ7.json","view_paper":"https://pith.science/paper/77P2PY3C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.01901&json=true","fetch_graph":"https://pith.science/api/pith-number/77P2PY3CF7UEOOTCJEMC5IZCQ7/graph.json","fetch_events":"https://pith.science/api/pith-number/77P2PY3CF7UEOOTCJEMC5IZCQ7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/77P2PY3CF7UEOOTCJEMC5IZCQ7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/77P2PY3CF7UEOOTCJEMC5IZCQ7/action/storage_attestation","attest_author":"https://pith.science/pith/77P2PY3CF7UEOOTCJEMC5IZCQ7/action/author_attestation","sign_citation":"https://pith.science/pith/77P2PY3CF7UEOOTCJEMC5IZCQ7/action/citation_signature","submit_replication":"https://pith.science/pith/77P2PY3CF7UEOOTCJEMC5IZCQ7/action/replication_record"}},"created_at":"2026-05-17T23:46:42.137378+00:00","updated_at":"2026-05-17T23:46:42.137378+00:00"}