Asymptotics of class number and genus for abelian extensions of an algebraic function field

TL;DR

This paper establishes an asymptotic relation between class number and genus for abelian extensions of a congruence function field, using classical methods from function field theory.

Contribution

It provides a new asymptotic relation specifically for abelian extensions of algebraic function fields, expanding understanding in this area.

Findings

Established an asymptotic relation between class number and genus.

Utilized classical congruence function field theory techniques.

Focused on abelian extensions of algebraic function fields.

Abstract

Among abelian extensions of a congruence function field, an asymptotic relation of class number and genus is established. The proof is classical, employing well-known results from congruence function field theory.