Monogenic trinomials with non-squarefree discriminant

被引：11
|
作者：
Jones, Lenny [1 ]
White, Daniel [2 ]
机构：
[1] Shippensbury Univ, Dept Math, 1871 Old Main Dr, Shippensburg, PA 17257 USA
[2] Bryn Mawr Coll, Dept Math, 101 North Merion Ave, Bryn Mawr, PA 19010 USA
来源：
INTERNATIONAL JOURNAL OF MATHEMATICS | 2021年 / 32卷 / 13期
关键词：
Monogenic; irreducible; trinomial; Galois group; INTEGRAL BASES; FREE VALUES; POLYNOMIALS; FIELDS; INDEX;
D O I：
10.1142/S0129167X21500890
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For each integer n >= 2, we identify new infinite families of monogenic trinomials f(x) = x(n) + Ax(m) + B with non-squarefree discriminant, many of which have small Galois group. Moreover, in certain situations when A = B >= 2 with fixed n and m, we produce asymptotics on the number of such trinomials with A <= X.
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页数：21
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