A counterexample to 'Algebraic function fields with small class number'

2013/11/25 by Claudio Stirpe, Stirpe, Claudio
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1311.6318

openalex publication_date 2013/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I give a counter example of function field over GF(2) of genus 4 with class number one. This result contradicts a previous result in [2], Section 2 so that proof is wrong.

Related

• Lower bounds on the class number of algebraic function fields defined over any finite field
• Function Fields of Class Number One
• Congruence Function Fields with Class Number One
• Classification of Algebraic Function Fields with Class Number One
• Class fields, Dirichlet characters and extended genus fields of global\n function fields