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Primitive Prime Divisors for Unicritical Polynomials

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posted on 01.11.2015, 00:00 by Holly C. Krieger
We prove the finiteness of the Zsigmondy set associated to critical orbits of polynomials. In the case of unicritical polynomials over the rational numbers, we find a uniform bound on the size of the Zsigmondy set. We prove further that there exists an effectively computable bound on the largest element of the Zsigmondy set, and that, under mild additional hypotheses, that bound is small.

History

Advisor

Takloo-Bighash, RaminDeMarco, Laura

Department

Mathematics, Statistics, and Computer Science

Degree Grantor

University of Illinois at Chicago

Degree Level

Doctoral

Committee Member

DeMarco, Laura Coskun, Izzet Hadian-Jazi, Majid Koch, Sarah

Submitted date

2013-08

Language

en

Issue date

31/10/2013

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