{"paper":{"title":"A property of a partial theta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Vladimir Petrov Kostov","submitted_at":"2015-04-07T08:58:09Z","abstract_excerpt":"The series $\\theta (q,x):=\\sum _{j=0}^{\\infty}q^{j(j+1)/2}x^j$ converges for $|q|<1$ and defines a {\\em partial theta function}. For any fixed $q\\in (0,1)$ it has infinitely many negative zeros. It is known that for $q$ taking one of the {\\em spectral} values $\\tilde{q}_1$, $\\tilde{q}_2$, $\\ldots$ (where $0.3092493386\\ldots =\\tilde{q}_1<\\tilde{q}_2<\\cdots <1$, $\\lim _{j\\rightarrow \\infty}\\tilde{q}_j=1$) the function $\\theta (q,.)$ has a double zero which is the rightmost of its real zeros (the rest of them being simple). For $q\\neq \\tilde{q}_j$ the partial theta function has no multiple real z"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01524","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"}