Matches in SemOpenAlex for { <https://semopenalex.org/work/W2074112081> ?p ?o ?g. }
Showing items 1 to 91 of
91
with 100 items per page.
- W2074112081 abstract "We give a method of constructing polynomials of arbitrarily large degree irreducible over a global field F but reducible modulo every prime of F. The method consists of finding quadratic f in F[x] whose iterates have the desired property, and it depends on new criteria ensuring all iterates of f are irreducible. In particular when F is a number field in which the ideal (2) is not a square, we construct infinitely many families of quadratic f such that every iterate f^n is irreducible over F, but f^n is reducible modulo all primes of F for n at least 2. We also give an example for each n of a quadratic f with integer coefficients whose iterates are all irreducible over the rationals, whose (n-1)st iterate is irreducible modulo some primes, and whose nth iterate is reducible modulo all primes. From the perspective of Galois theory, this suggests that a well-known rigidity phenomenon for linear Galois representations does not exist for Galois representations obtained by polynomial iteration. Finally, we study the number of primes P for which a given quadratic f defined over a global field has f^n irreducible modulo P for all n." @default.
- W2074112081 created "2016-06-24" @default.
- W2074112081 creator A5001570714 @default.
- W2074112081 date "2010-12-13" @default.
- W2074112081 modified "2023-09-27" @default.
- W2074112081 title "An iterative construction of irreducible polynomials reducible modulo every prime" @default.
- W2074112081 cites W1567904287 @default.
- W2074112081 cites W1594510786 @default.
- W2074112081 cites W2017322818 @default.
- W2074112081 cites W2022523627 @default.
- W2074112081 cites W2027147916 @default.
- W2074112081 cites W2071069063 @default.
- W2074112081 cites W2072788806 @default.
- W2074112081 cites W2077554156 @default.
- W2074112081 cites W2080305479 @default.
- W2074112081 cites W2226303357 @default.
- W2074112081 cites W54228656 @default.
- W2074112081 hasPublicationYear "2010" @default.
- W2074112081 type Work @default.
- W2074112081 sameAs 2074112081 @default.
- W2074112081 citedByCount "2" @default.
- W2074112081 countsByYear W20741120812012 @default.
- W2074112081 crossrefType "posted-content" @default.
- W2074112081 hasAuthorship W2074112081A5001570714 @default.
- W2074112081 hasConcept C101044782 @default.
- W2074112081 hasConcept C114614502 @default.
- W2074112081 hasConcept C118615104 @default.
- W2074112081 hasConcept C129844170 @default.
- W2074112081 hasConcept C134306372 @default.
- W2074112081 hasConcept C140479938 @default.
- W2074112081 hasConcept C15376144 @default.
- W2074112081 hasConcept C165030954 @default.
- W2074112081 hasConcept C183877218 @default.
- W2074112081 hasConcept C184992742 @default.
- W2074112081 hasConcept C199360897 @default.
- W2074112081 hasConcept C202444582 @default.
- W2074112081 hasConcept C2524010 @default.
- W2074112081 hasConcept C33923547 @default.
- W2074112081 hasConcept C41008148 @default.
- W2074112081 hasConcept C5106717 @default.
- W2074112081 hasConcept C51568863 @default.
- W2074112081 hasConcept C54732982 @default.
- W2074112081 hasConcept C90119067 @default.
- W2074112081 hasConcept C97137487 @default.
- W2074112081 hasConceptScore W2074112081C101044782 @default.
- W2074112081 hasConceptScore W2074112081C114614502 @default.
- W2074112081 hasConceptScore W2074112081C118615104 @default.
- W2074112081 hasConceptScore W2074112081C129844170 @default.
- W2074112081 hasConceptScore W2074112081C134306372 @default.
- W2074112081 hasConceptScore W2074112081C140479938 @default.
- W2074112081 hasConceptScore W2074112081C15376144 @default.
- W2074112081 hasConceptScore W2074112081C165030954 @default.
- W2074112081 hasConceptScore W2074112081C183877218 @default.
- W2074112081 hasConceptScore W2074112081C184992742 @default.
- W2074112081 hasConceptScore W2074112081C199360897 @default.
- W2074112081 hasConceptScore W2074112081C202444582 @default.
- W2074112081 hasConceptScore W2074112081C2524010 @default.
- W2074112081 hasConceptScore W2074112081C33923547 @default.
- W2074112081 hasConceptScore W2074112081C41008148 @default.
- W2074112081 hasConceptScore W2074112081C5106717 @default.
- W2074112081 hasConceptScore W2074112081C51568863 @default.
- W2074112081 hasConceptScore W2074112081C54732982 @default.
- W2074112081 hasConceptScore W2074112081C90119067 @default.
- W2074112081 hasConceptScore W2074112081C97137487 @default.
- W2074112081 hasLocation W20741120811 @default.
- W2074112081 hasOpenAccess W2074112081 @default.
- W2074112081 hasPrimaryLocation W20741120811 @default.
- W2074112081 hasRelatedWork W1520938943 @default.
- W2074112081 hasRelatedWork W1549813660 @default.
- W2074112081 hasRelatedWork W1578450251 @default.
- W2074112081 hasRelatedWork W1660891760 @default.
- W2074112081 hasRelatedWork W1976936138 @default.
- W2074112081 hasRelatedWork W2003573719 @default.
- W2074112081 hasRelatedWork W2007095311 @default.
- W2074112081 hasRelatedWork W2058177166 @default.
- W2074112081 hasRelatedWork W2059208884 @default.
- W2074112081 hasRelatedWork W2079794257 @default.
- W2074112081 hasRelatedWork W2083023693 @default.
- W2074112081 hasRelatedWork W2940414383 @default.
- W2074112081 hasRelatedWork W2953273942 @default.
- W2074112081 hasRelatedWork W2953390031 @default.
- W2074112081 hasRelatedWork W2963739610 @default.
- W2074112081 hasRelatedWork W3017334286 @default.
- W2074112081 hasRelatedWork W3105226291 @default.
- W2074112081 hasRelatedWork W3135641670 @default.
- W2074112081 hasRelatedWork W3190755058 @default.
- W2074112081 hasRelatedWork W2098174412 @default.
- W2074112081 isParatext "false" @default.
- W2074112081 isRetracted "false" @default.
- W2074112081 magId "2074112081" @default.
- W2074112081 workType "article" @default.