{"paper":{"title":"On the zeros of Confluent Hypergeometric Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CV","math.MP"],"primary_cat":"math.CA","authors_text":"Wei-Chuan Lin, Xu-Dan Luo","submitted_at":"2015-10-05T19:06:57Z","abstract_excerpt":"In this paper, we study the zero sets of the confluent hypergeometric function $_{1}F_{1}(\\alpha;\\gamma;z):=\\sum_{n=0}^{\\infty}\\frac{(\\alpha)_{n}}{n!(\\gamma)_{n}}z^{n}$, where $\\alpha, \\gamma, \\gamma-\\alpha\\not\\in \\mathbb{Z}_{\\leq 0}$, and show that if $\\{z_n\\}_{n=1}^{\\infty}$ is the zero set of $_{1}F_{1}(\\alpha;\\gamma;z)$ with multiple zeros repeated and modulus in increasing order, then there exists a constant $M>0$ such that $|z_n|\\geq M n$ for all $n\\geq 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01285","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"}