{"paper":{"title":"On the necessary condition for entire function with the increasing second quotients of Taylor coefficients to belong to the Laguerre-P\\'olya class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Anna Vishnyakova, Thu Hien Nguyen","submitted_at":"2019-03-21T15:47:44Z","abstract_excerpt":"For an entire function $f(z) = \\sum_{k=0}^\\infty a_k z^k, a_k>0,$ we show that $f$ does not belong to the Laguerre-P\\'olya class if the quotients $\\frac{a_{n-1}^2}{a_{n-2}a_n}$ are increasing in $n$, and $c:= \\lim\\limits_{n\\to \\infty} \\frac{a_{n-1}^2}{a_{n-2}a_n}$ is smaller than an absolute constant $q_\\infty$ $(q_\\infty\\approx 3{.}2336) .$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09070","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"}