Ray class fields of global function fields with many rational places
Roland Auer
TL;DR
This paper investigates ray class fields of global function fields, systematically computes their genera, and provides new examples of algebraic curves over finite fields with many rational points.
Contribution
It introduces a general framework for ray class fields in global function fields and computes their genera to find new curves with many rational points.
Findings
New examples of curves with many rational points over finite fields
Systematic computation of genera of ray class fields
Enhanced understanding of function field extensions
Abstract
A general type of ray class fields of global function fields is investigated. The systematic computation of their genera leads to new examples of curves over finite fields with comparatively many rational points.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Coding theory and cryptography · Advanced Algebra and Geometry