Indivisibility of divisor class numbers of Kummer extensions over the rational function field

Yoonjin Lee, Jinjoo Yoo

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We find a complete criterion for a Kummer extension K over the rational function field k=Fq(T) of degree ℓ to have indivisibility of its divisor class number hK by ℓ where Fq is the finite field of order q and ℓ is a prime divisor of q−1. More importantly, when hK is not divisible by ℓ we have hK≡1(modℓ). In fact, the indivisibility of hK by ℓ depends on the number of finite primes ramified in K/k and whether or not the infinite prime of k is unramified in K. Using this criterion, we explicitly construct an infinite family of the maximal real cyclotomic function fields whose divisor class numbers are divisible by ℓ.

Original languageEnglish
Pages (from-to)270-292
Number of pages23
JournalJournal of Number Theory
Volume192
DOIs
StatePublished - Nov 2018

Keywords

  • Class number
  • Cyclotomic function field
  • Global function field
  • Kummer extension

Fingerprint

Dive into the research topics of 'Indivisibility of divisor class numbers of Kummer extensions over the rational function field'. Together they form a unique fingerprint.

Cite this