Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896981 | Journal of Number Theory | 2018 | 43 Pages |
Abstract
For every nonconstant polynomial fâQ[x], let Φ4,f denote the fourth dynatomic polynomial of f. We determine here the structure of the Galois group and the degrees of the irreducible factors of Φ4,f for every quadratic polynomial f. As an application we prove new results related to a uniform boundedness conjecture of Morton and Silverman. In particular we show that if f is a quadratic polynomial, then, for more than 39% of all primes p, f does not have a point of period four in Qp.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
David Krumm,