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Manuscripta Mathematica

, Volume 137, Issue 3–4, pp 273–286 | Cite as

Ramification in iterated towers for rational functions

  • John CullinanEmail author
  • Farshid Hajir
Article

Abstract

Let \({\phi(x)}\) be a rational function of degree > 1 defined over a number field K and let \({\Phi_{n}(x,t) = \phi^{(n)}(x)-t \in K(x,t)}\) where \({\phi^{(n)}(x)}\) is the nth iterate of \({\phi(x)}\). We give a formula for the discriminant of the numerator of Φ n (x, t) and show that, if \({\phi(x)}\) is postcritically finite, for each specialization t 0 of t to K, there exists a finite set \({S_{t_0}}\) of primes of K such that for all n, the primes dividing the discriminant are contained in \({S_{t_0}}\).

Keywords

Rational Function Branch Point Elliptic Curve Galois Group Prime Divisor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsBard CollegeAnnandale-On-HudsonUSA
  2. 2.Department of MathematicsUniversity of Massachusetts AmherstAmherstUSA

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