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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","authors_text":"Vladimir Petrov Kostov","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-04-06T15:58:42Z","title":"A separation in modulus property of the zeros of a partial theta function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01901","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:185d5f947e40f024c48fcc594104e58c2da192211005bd7597c98d7abf174cee","target":"record","created_at":"2026-05-17T23:46:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c8d2ada4fafaf25ae6c8d54f98b01d59a8d08328dd19541a5585883420c87f78","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-04-06T15:58:42Z","title_canon_sha256":"6de6171189f03722a9f92fe7db793dfbe7f327e918a295bf02a407184bc09dce"},"schema_version":"1.0","source":{"id":"1704.01901","kind":"arxiv","version":1}},"canonical_sha256":"ffdfa7e3622fe8473a6249182ea32287f3f1dd266b04c8cd8089508da4499a20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffdfa7e3622fe8473a6249182ea32287f3f1dd266b04c8cd8089508da4499a20","first_computed_at":"2026-05-17T23:46:42.137249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:42.137249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5tX6ptufpQj/DXzGORAYSac83PHHwsG1/Ow718T5N1Gc0x7Grf15ybXU934KosuDF8r7oYp9IaTpcrDAM71yDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:42.137954Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.01901","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:185d5f947e40f024c48fcc594104e58c2da192211005bd7597c98d7abf174cee","sha256:322435cac798827a024904d703f730e3d41d89da592233b03e22a14db441e480"],"state_sha256":"1006721ffe6f0f10d3f5c385becb55477807e9d356184932f731319c531efac0"}