Zeta functions of quadratic Artin-Schreier curves in characteristic two
R\'egis Blache (LAMIA), Timoth\'e Pierre (UEH)
TL;DR
This paper investigates the invariants of quadratic forms over finite fields of characteristic two and explores the zeta functions of specific Artin-Schreier curves, connecting algebraic invariants with curve properties.
Contribution
It provides new insights into the invariants of quadratic forms in characteristic two and advances understanding of the zeta functions of certain Artin-Schreier curves.
Findings
Characterization of quadratic form invariants in characteristic two
Results on zeta functions of specific Artin-Schreier curves
Connections between quadratic form invariants and curve zeta functions
Abstract
The aim of this paper is twofold: on one hand we study the invariants of traces of quadratic forms over a finite field of characteristic two. On the other hand, we give results about the zeta functions of certain curves studied by van der Geer and ven der Vlugt.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Analytic Number Theory Research