{"paper":{"title":"On a partial theta function and its spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Vladimir Petrov Kostov","submitted_at":"2015-04-22T13:38:16Z","abstract_excerpt":"The bivariate series $\\theta (q,x):=\\sum _{j=0}^{\\infty}q^{j(j+1)/2}x^j$ %(where $(q,x)\\in {\\bf C}^2$, $|q|<1$) defines a {\\em partial theta function}. For fixed $q$ ($|q|<1$), $\\theta (q,.)$ is an entire function. For $q\\in (-1,0)$ the function $\\theta (q,.)$ has infinitely many negative and infinitely many positive real zeros. There exists a sequence $\\{ \\bar{q}_j\\}$ of values of $q$ tending to $-1^+$ such that $\\theta (\\bar{q}_k,.)$ has a double real zero $\\bar{y}_k$ (the rest of its real zeros being simple). For $k$ odd (resp. for $k$ even) $\\theta (\\bar{q}_k,.)$ has a local minimum at $\\b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05798","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"}