{"paper":{"title":"Where not to find the spectrum of the partial theta function","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Vladimir Petrov Kostov, Yousra Gati","submitted_at":"2026-05-28T13:23:39Z","abstract_excerpt":"The spectrum of Ramanujan's partial theta function $\\theta (q,x):=\\sum _{j=0}^{\\infty}q^{j(j+1)/2}x^j$, $q\\in \\mathbb{D}_1$ (the unit disk centered at the origin), $x\\in \\mathbb{C}$, is the set of values of the parameter $q$ for which $\\theta (q,.)$ has a multiple zero. We show that there is no spectral value in the set $\\mathbb{S}\\cup \\mathbb{D}_{c_0}$, $c_0=0.2078750206\\ldots$, where $\\mathbb{S}$ is the sector $\\{ 0<|z|<0.6,{\\rm arg}(z)\\in [\\pi /4 ,7\\pi /4 ]\\}$. There is a single spectral value in the set $\\mathbb{S}\\cup \\mathbb{D}_{0.31}$ which equals $0.309249\\ldots$. For $q\\in \\mathbb{S}\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29903","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/2605.29903/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"}