170468 20260422085545.0 sideral 148961 ART-2023-148961 eng Cantero Medina, María José Universidad de Zaragoza (orcid)0000-0003-3636-276X On skyburst polynomials and their zeros 2023 We consider polynomials orthogonal on the unit circle with respect to the complex-valued measure z ω−1 dz, where ω ∈ R\ {0}. We derive their explicit form, a generating function and several recurrence relations. These polynomials possess an intriguing pattern of zeros which, as ω varies, are reminiscent of a firework explosion. We prove this pattern in a rigorous manner. Access copy available to the general public Unrestricted info:eu-repo/grantAgreement/ES/DGA/E48-23R info:eu-repo/grantAgreement/ES/MICINN/PID2021-124472NB-I00 info:eu-repo/semantics/openAccess by-nc-nd https://creativecommons.org/licenses/by-nc-nd/4.0/deed.es 0.417 2023 Mathematics (miscellaneous) 2023 Q2 Applied Mathematics 2023 Q3 1.7 2023 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Iserles, Arieh 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 16, 1 (2023), 31-41 Dolomites Research Notes on Approximation 2035-6803 536847 http://zaguan.unizar.es/record/170468/files/texto_completo.pdf Versión publicada 2230352 http://zaguan.unizar.es/record/170468/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:170468 articulos driver 2026-04-22-08:33:03 ARTICLE