{"paper":{"title":"Ap\\'ery Polynomials and the multivariate Saddle Point Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Thorsten Neuschel","submitted_at":"2013-07-01T12:10:52Z","abstract_excerpt":"The Ap\\'ery polynomials and in particular their asymptotic behavior play an essential role in the understanding of the irrationality of \\zeta(3). In this paper, we present a method to study the asymptotic behavior of the sequence of the Ap\\'ery polynomials ((B_{n})_{n=1}^{\\infty}) in the whole complex plane as (n\\rightarrow \\infty). The proofs are based on a multivariate version of the complex saddle point method. Moreover, the asymptotic zero distributions for the polynomials ((B_{n})_{n=1}^{\\infty}) and for some transformed Ap\\'ery polynomials are derived by means of the theory of logarithmi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0341","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"}