{"paper":{"title":"Uniform bounds on locations of zeros of partial theta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Vladimir Petrov Kostov","submitted_at":"2016-07-19T08:25:00Z","abstract_excerpt":"We consider the partial theta function $\\theta (q,z):=\\sum _{j=0}^{\\infty}q^{j(j+1)/2}z^j$, where $(q,z)\\in \\mathbb{C}^2$, $|q|<1$. We show that for any $0<\\delta _0<\\delta <1$, there exists $n_0\\in \\mathbb{N}$ such that for any $q$ with $\\delta _0\\leq |q|\\leq \\delta$ and for any $n\\geq n_0$ the function $\\theta$ has exactly $n$ zeros with modulus $<|q|^{-n-1/2}$ counted with multiplicity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05453","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"}