L-functions of curves of genus ≥ 3
Dissertation
Autoren
Börner, Michel
Gutachter
Wewers, StefanSijsling, Jeroen
Fakultäten
Fakultät für Mathematik und WirtschaftswissenschaftenInstitutionen
Institut für Reine MathematikZusammenfassung
We introduce an algorithm (written in Sage) for the L-functions of a large class of algebraic curves,
and verify the expected functional equation numerically. Our computations
are based on our previous results on stable reduction to calculate the
local L-factor and the conductor exponent at the primes of bad reduction.
The method we use works for any superelliptic curve over a number field.
We present several families of examples, e.g. hyperelliptic curves
of genus 2,...,6 with semistable reduction everywhere.
In a second part, we consider Picard curves over Q. We give a completed list of the curves resulting from the algorithm by Malmskog and Rasmussen. Moreover, we present generalizations of their approach. This leads to a recipe for the calculation of the smallest conductor of a Picard curve over Q.
Erstellung / Fertigstellung
2016
Förderinformationen
SPP 1489//Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory
DFG
DFG
Normierte Schlagwörter
Algebra [GND]Kurve [GND]
L-Funktion [GND]
Algebraische Geometrie [GND]
Geometry, algebraic [LCSH]
Curves, algebraic [LCSH]
L-functions [LCSH]
DDC-Sachgruppe
DDC 510 / MathematicsMetadata
Zur LanganzeigeZitiervorlage
Börner, Michel (2016): L-functions of curves of genus ≥ 3. Open Access Repositorium der Universität Ulm. Dissertation. http://dx.doi.org/10.18725/OPARU-4137