One Level Density for Cubic Galois Number Fields

Class-number Problems for Cubic Number Fields

Procyclic Galois Extensions of Algebraic Number Fields

6 1 Iwasawa’s theory of Zp-extensions 9 1.

Class number approximation in cubic function fields

A central problem in number theory and algebraic geometry is the determination of the size of the group of rational points on the Jacobian of an algebraic curve over a finite field. This question also has applications to cryptography, since cryptographic systems based on algebraic curves generally require a Jacobian of non-smooth order in order to foil certain types of attacks. There a variety ...

Stark's conjecture over complex cubic number fields

Systematic computation of Stark units over nontotally real base fields is carried out for the first time. Since the information provided by Stark’s conjecture is significantly less in this situation than the information provided over totally real base fields, new techniques are required. Precomputing Stark units in relative quadratic extensions (where the conjecture is already known to hold) an...

Binomial squares in pure cubic number fields

Let K = Q(ω), with ω3 = m a positive integer, be a pure cubic number field. We show that the elements α ∈ K× whose squares have the form a − ω for rational numbers a form a group isomorphic to the group of rational points on the elliptic curve Em : y2 = x3 − m. This result will allow us to construct unramified quadratic extensions of pure cubic number fields K.