{"paper":{"title":"Brenke polynomials with real zeros and the Riemann Hypothesis","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.CV","math.NT"],"primary_cat":"math.CA","authors_text":"Antonio J. Dur\\'an","submitted_at":"2024-05-29T09:49:25Z","abstract_excerpt":"If $A(z)=\\sum_{n=0}^\\infty a_nz^n$ and $B(z)=\\sum_{n=0}^\\infty b_nz^n$ are two formal power series, with $a_n,b_n\\in \\mathbb{R}$, the polynomials $(p_n)_n$ defined by the generating function $$ A(z)B(xz)=\\sum_{n=0}^\\infty p_n(x)z^n $$ are called the Brenke polynomials generated by $A$ and associated to $B$. We say that $A\\in \\mathcal{R}_B$ if the Brenke polynomials $(p_n)_n$ have only real zeros. Among other results, in this paper we find necessary and sufficient conditions on $B$ such that $\\mathcal{R}_B=\\mathcal{L}\\text{-}\\mathcal{P}$, where $\\mathcal{L}\\text{-}\\mathcal{P}$ denotes the Lague"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.18940","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.18940/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}