{"paper":{"title":"Complex spectrum of the partial theta function","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"Boris Shapiro","submitted_at":"2026-05-28T14:24:37Z","abstract_excerpt":"We study the complex spectrum of the partial theta function \\[\n  \\Theta(q,x)=\\sum_{j=0}^{\\infty}q^{j(j+1)/2}x^j,\n  \\qquad |q|<1, \\] where a spectral value is a parameter for which \\(\\Theta(q,\\cdot)\\) has a multiple zero. Since the function is defined here only for \\(|q|<1\\), all spectral values are strictly inside the unit disk; boundary points on \\(|q|=1\\) occur only as accumulation points of the spectrum. The paper combines two complementary points of view. Near the unit circle we prove that every point of \\(|q|=1\\) is an accumulation point of the spectrum; the proof uses explicit spectral f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29991","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.29991/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}