On irreducible divisors of iterated polynomials

D. Gómez-Pérez, A. Ostafe, A.P. Nicolás and D. Sadornil have recently shown that for almost all polynomials f?Fq[X]f?Fq[X] over the finite field of qq elements, where qq is an odd prime power, their iterates eventually become reducible polynomials over FqFq. Here we combine their method with some ne...

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Detalles Bibliográficos
Autores: Gómez Pérez, Domingo|||0000-0002-5780-2165, Ostafe, Alina, Shparlinski, Igor E.
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/8026
Acceso en línea:http://hdl.handle.net/10902/8026
Access Level:acceso abierto
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spelling On irreducible divisors of iterated polynomialsGómez Pérez, Domingo|||0000-0002-5780-2165Ostafe, AlinaShparlinski, Igor E.D. Gómez-Pérez, A. Ostafe, A.P. Nicolás and D. Sadornil have recently shown that for almost all polynomials f?Fq[X]f?Fq[X] over the finite field of qq elements, where qq is an odd prime power, their iterates eventually become reducible polynomials over FqFq. Here we combine their method with some new ideas to derive finer results about the arithmetic structure of iterates of ff. In particular, we prove that the nnth iterate of ff has a square-free divisor of degree of order at least n1+o(1)n1+o(1) as n?8n?8 (uniformly in qq).European Mathematical Society, para la Real Sociedad Matemática EspañolaUniversidad de Cantabria20142014-01-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttp://hdl.handle.net/10902/8026Revista matemática iberoamericana, Vol. 30, Nº 4, págs. 1123-1134reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.unican.es:10902/80262026-06-02T12:39:31Z
dc.title.none.fl_str_mv On irreducible divisors of iterated polynomials
title On irreducible divisors of iterated polynomials
spellingShingle On irreducible divisors of iterated polynomials
Gómez Pérez, Domingo|||0000-0002-5780-2165
title_short On irreducible divisors of iterated polynomials
title_full On irreducible divisors of iterated polynomials
title_fullStr On irreducible divisors of iterated polynomials
title_full_unstemmed On irreducible divisors of iterated polynomials
title_sort On irreducible divisors of iterated polynomials
dc.creator.none.fl_str_mv Gómez Pérez, Domingo|||0000-0002-5780-2165
Ostafe, Alina
Shparlinski, Igor E.
author Gómez Pérez, Domingo|||0000-0002-5780-2165
author_facet Gómez Pérez, Domingo|||0000-0002-5780-2165
Ostafe, Alina
Shparlinski, Igor E.
author_role author
author2 Ostafe, Alina
Shparlinski, Igor E.
author2_role author
author
dc.contributor.none.fl_str_mv Universidad de Cantabria
description D. Gómez-Pérez, A. Ostafe, A.P. Nicolás and D. Sadornil have recently shown that for almost all polynomials f?Fq[X]f?Fq[X] over the finite field of qq elements, where qq is an odd prime power, their iterates eventually become reducible polynomials over FqFq. Here we combine their method with some new ideas to derive finer results about the arithmetic structure of iterates of ff. In particular, we prove that the nnth iterate of ff has a square-free divisor of degree of order at least n1+o(1)n1+o(1) as n?8n?8 (uniformly in qq).
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10902/8026
url http://hdl.handle.net/10902/8026
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv European Mathematical Society, para la Real Sociedad Matemática Española
publisher.none.fl_str_mv European Mathematical Society, para la Real Sociedad Matemática Española
dc.source.none.fl_str_mv Revista matemática iberoamericana, Vol. 30, Nº 4, págs. 1123-1134
reponame:UCrea Repositorio Abierto de la Universidad de Cantabria
instname:Universidad de Cantabria (UC)
instname_str Universidad de Cantabria (UC)
reponame_str UCrea Repositorio Abierto de la Universidad de Cantabria
collection UCrea Repositorio Abierto de la Universidad de Cantabria
repository.name.fl_str_mv
repository.mail.fl_str_mv
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