3 papers
math.NT2020
Normal CM-fields with class number one
Tommy Hofmann, Carlo Sircana
We show that assuming the generalized Riemann hypothesis there are no normal CM-fields with class number one of degree 64 and 96. This is done by constructing complete tables of no…
cs.SC2020
Resultants over principal Artinian rings
Claus Fieker, Tommy Hofmann, Carlo Sircana
The resultant of two univariate polynomials is an invariant of great importance in commutative algebra and vastly used in computer algebra systems. Here we present an algorithm to…
math.NT2019
On the computation of overorders
Tommy Hofmann, Carlo Sircana
The computation of a maximal order of an order in a semisimple algebra over a global field is a classical well-studied problem in algorithmic number theory. In this paper we consid…