research

Research Interests

My field of interest is Number Theory, in particular Algebraic Number Theory with a focus on explicit and computational methods. Research topics include the following:
  • Elliptic curves, in particular over finite fields,
  • Explicit formulas for zeta functions of modules over integral group rings, and applications in Number Theory,
  • Distribution of p-class groups of cyclic number fields of odd prime degree p.
Currently I am working on l-class groups of cyclic extensions of degree l of the rational function field Fq(T), where l is a prime number not dividing q. The goal is to understand the Galois module structure of these l-class groups, and to obtain density results (this will include heuristic methods, too).
Here are some tables containing
  • Explicit formulas for zeta functions,
  • 3-class groups of cyclic cubic number field extensions with prescribed ramification.