Krieger_Holly.pdf (446.92 kB)
Primitive Prime Divisors for Unicritical Polynomials
thesisposted on 2015-11-01, 00:00 authored 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.
AdvisorTakloo-Bighash, RaminDeMarco, Laura
DepartmentMathematics, Statistics, and Computer Science
Degree GrantorUniversity of Illinois at Chicago
Committee MemberDeMarco, Laura Coskun, Izzet Hadian-Jazi, Majid Koch, Sarah