Papers › Galois groups in a family of dynatomic polynomials
Galois groups in a family of dynatomic polynomials
David Krumm
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For every nonconstant polynomial f∈ℚ[x], let Φ_(4,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 Φ_(4,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.
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