Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10224089 | Journal of Number Theory | 2018 | 23 Pages |
Abstract
We find a complete criterion for a Kummer extension K over the rational function field k=Fq(T) of degree â to have indivisibility of its divisor class number hK by â, where Fq is the finite field of order q and â is a prime divisor of qâ1. More importantly, when hK is not divisible by â, we have hKâ¡1(modâ). In fact, the indivisibility of hK by â 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 â.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Yoonjin Lee, Jinjoo Yoo,