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Prime divisors in polynomial orbits over function fields
Author(s) -
Hindes Wade
Publication year - 2016
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdw061
Subject(s) - mathematics , prime (order theory) , iterated function , base (topology) , polynomial , field (mathematics) , function (biology) , function field , orbit (dynamics) , quadratic function , pure mathematics , combinatorics , discrete mathematics , quadratic equation , mathematical analysis , geometry , evolutionary biology , engineering , biology , aerospace engineering
Given a polynomial ϕ over a global function field K / F q ( t )and a wandering base point b ∈ K , we give a geometric condition on ϕ , ensuring the existence of primitive prime divisors for almost all points in the orbitO ϕ ( b ) : = { ϕ n ( b ) } n ⩾ 0. As an application, we prove that the Galois groups (over K ) of the iterates of many quadratic polynomials are large and use this to compute the density of prime divisors ofO ϕ ( b ) .
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