Function Fields with Class Number Indivisible by a Prime $\ell$

Details Function Fields with Class Number Indivisible by a Prime $\ell$ Function Fields with Class Number Indivisible by a Prime $\ell$

2009-06-19

arxiv.org/abs/0906.3728v1

Mathematics

Number Theory

Scientific paper

It is known that infinitely many number fields and function fields of any degree $m$ have class number divisible by a given integer $n$. However, significantly less is known about the indivisibility of class numbers of such fields. While it's known that there exist infinitely many quadratic number fields with class number indivisible by a given prime, the fields are not constructed explicitly, and nothing appears to be known for higher degree extensions. In \cite{Pacelli-Rosen}, Pacelli and Rosen explicitly constructed an infinite class of function fields of any degree $m$, $3 \nmid m$, over $\F_q(T)$ with class number indivisible by 3, generalizing a result of Ichimura for quadratic extensions. Here we generalize that result, constructing, for an arbitrary prime $\ell$, and positive integer $m > 1$, infinitely many function fields of degree $m$ over the rational function field, with class number indivisible by $\ell$.

Affiliated with

Also associated with

No associations

Rating

Function Fields with Class Number Indivisible by a Prime $\ell$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Function Fields with Class Number Indivisible by a Prime $\ell$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Function Fields with Class Number Indivisible by a Prime $\ell$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-402192