The Spiegelungssatz for p=5 from a Constructive Approach

We describe explicitly the relation between the 5-ranks of the ideal class groups of two quadratic fields with conductors m and 5m, respectively, and that of the associated cyclic quartic field.</p

Construction of families of dihedral quintic polynomials

In this article, we give two families of dihedral quintic polynomials by using the Weber sextic resolvent and a certain elliptic curve

Divisibility of the class numbers of imaginary quadratic fields

For a given odd integer $n>1$, we provide some families of imaginary quadratic number fields of the form $\mathbb{Q}(\sqrt{x^2-t^n})$ whose ideal class group has a subgroup isomorphic to $\mathbb{Z}/n\mathbb{Z}$.Comment: 10 pages, accepted for publication in Journal of Number Theory (2017

A remark on the Lavallee-Spearman-Williams-Yang family of quadratic fields

In [4], M. J. Lavallee, B. K. Spearman, K. S. Williams and Q. Yang introduced a certain parametric D5-quintic polynomial and studied its splitting field. The present paper gives an infinite family of quadratic fields with class number divisible by 5 by using properties of its polynomial