On Artin L-functions and Gassmann Equivalence for Global Function Fields
arXiv:1610.05600
Abstract
In this paper we present an approach to study arithmetical properties of global function fields by working with Artin L-functions. In particular we recall and then extend a criteria of two function fields to be arithmetically equivalent in terms of Artin L-functions of representations associated to the common normal closure of those fields. We provide few examples of such non-isomorphic fields and also discuss an algorithm to construct many such examples by using torsion points on elliptic curves. Finally, we will show how to apply our results in order to distinguish two global fields by a finite list of Artin L-functions.
20 pages, a mistake in the section 3.1.2 was fixed
Cited by in corpus (3)
- Reconstructing global fields from Dirichlet L-series
- A Note on Number Fields Sharing the List of Dedekind Zeta-Functions of Abelian Extensions with some Applications towards the Neukirch-Uchida Theorem
- Notes on Explicit Constructions of Arithmetically Equivalent Global Function Fields via Torsion Points On Drinfeld Modules