1. CMB 2002 (vol 45 pp. 138)
|The Discriminant of a Dihedral Quintic Field Defined by a Trinomial $X^5 + aX + b$ |
Let $X^5 + aX + b \in Z[X]$ have Galois group $D_5$. Let $\theta$ be a root of $X^5 + aX + b$. An explicit formula is given for the discriminant of $Q(\theta)$.
Keywords:dihedral quintic field, trinomial, discriminant
2. CMB 1998 (vol 41 pp. 158)
|Power integral bases in composits of number fields |
In the present paper we consider the problem of finding power integral bases in number fields which are composits of two subfields with coprime discriminants. Especially, we consider imaginary quadratic extensions of totally real cyclic number fields of prime degree. As an example we solve the index form equation completely in a two parametric family of fields of degree $10$ of this type.