{"paper":{"title":"A separation in modulus property of the zeros of a partial theta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"Vladimir Petrov Kostov","submitted_at":"2017-04-06T15:58:42Z","abstract_excerpt":"We consider the partial theta function $\\theta (q,z):=\\sum _{j=0}^{\\infty}q^{j(j+1)/2}z^j$, where $z\\in \\mathbb{C}$ is a variable and $q\\in \\mathbb{C}$, $0<|q|<1$, is a parameter. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01901","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"}