Galois groups in a family of dynatomic polynomials

被引：3

作者：

Krumm, David ^{[1
]}

机构：

[1] Colby Coll, Dept Math & Stat, Waterville, ME 04901 USA

来源：

JOURNAL OF NUMBER THEORY | 2018年 / 187卷

关键词：

Arithmetic dynamics; Hilbert irreducibility theorem; Method of Chabauty and Coleman; PERIODIC POINTS; QUADRATIC POLYNOMIALS; ARITHMETIC PROPERTIES; HYPERELLIPTIC CURVES; MAPS;

D O I：

10.1016/j.jnt.2017.11.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For every nonconstant polynomial f is an element of Q[x], let Phi(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 Phi(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 Q(p). (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：469 / 511

页数：43