Section: New Results
Class groups and other invariants of number fields
The article by H. Cohen and F. Thorne
on Dirichlet series associated to quartic fields with given
cubic resolvent has been published.
This article gives an explicit formula for the
Dirichlet series
The article [22] by H. Cohen and F. Thorne
generalizes the work of A. Morra and the authors, on giving explicit formulas for the Dirichlet series generating function of
In her thesis, Iuliana Ciocanea-Teodorescu describes algorithms that answer questions arising in ring and module theory. The first main result of this thesis concerns the module isomorphism problem, how to compute a set of generators of minimal cardinality, and how to construct projective covers and injective hulls. The thesis also describe tests for module simplicity, projectivity, and injectivity, and constructive tests for existence of surjective module homomorphisms between two finite modules, one of which is projective. As a negative result, the problem of testing for existence of injective module homomorphisms between two finite modules, one of which is projective, is NP-complete. The last part of the thesis is concerned with finding a good working approximation of the Jacobson radical of a finite ring, that is, a two-sided nilpotent ideal such that the corresponding quotient ring is almost semisimple. The notion used to approximate semisimplicity is that of separability.
In her thesis [11], Pinar Kiliçer determines all CM curves of genus 2 defined over the reflex field. This extends the previous CM class number one problem for elliptic curves which asked to find all elliptic curves defined over the rationals with non-trivial endomorphism ring.