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3-class field towers with 2 or 3 stages
Helga Boyer von Berghof, Daniel C. Mayer
For quadratic fields \(k=\mathbb{Q}(\sqrt{d})\) with discriminant \(d\), \(3\)-class group \(\mathrm{Cl}_3(k)\simeq (\mathbb{Z}/3\mathbb{Z})^2\), and four \textit{simple} \(3\)-pri…
Coclass of the second 3-class group
Siham Aouissi, Daniel C. Mayer
By means of parametrized presentations of finite metabelian 3-groups, it is proved that the coclass cc(M) of the second 3-class group M=Gal(F_3^2(K)/K) of any algebraic number fiel…
The Capitulation Problem in Certain Pure Cubic Fields
Siham Aouissi, Daniel C. Mayer
Let \(Γ=\mathbb{Q}(\sqrt[3]{n})\) be a pure cubic field with normal closure \(k=\mathbb{Q}(\sqrt[3]{n},ζ)\), where \(n>1\) denotes a cube free integer, and \(ζ\) is a primitive cub…
Some results about entropy and divergence in number theory
Daniel C. Mayer, Nicusor Minculete, Diana Savin +1
We obtain inequalities involving the entropy of a positive integer and the divergence of two positive integers, respectively the entropy of an ideal and the divergence of two ideal…
Group theory of cyclic cubic number fields
Daniel C. Mayer, Siham Aouissi, Bill Allombert +1
Astonishing new discoveries with quartets and octets of cyclic cubic fields sharing a common conductor are presented. Four kinds of graphs describing cubic residue conditions among…