## Involve: A Journal of Mathematics

• Involve
• Volume 1, Number 1 (2008), 47-58.

### Divisibility of class numbers of imaginary quadratic function fields

#### Abstract

We consider applications to function fields of methods previously used to study divisibility of class numbers of quadratic number fields. Let $K$ be a quadratic extension of $Fq(x)$, where $q$ is an odd prime power. We first present a function field analog to a Diophantine method of Soundararajan for finding quadratic imaginary function fields whose class groups have elements of a given order. We also show that this method does not miss many such fields. We then use a method similar to Hartung to show that there are infinitely many imaginary $K$ whose class numbers are indivisible by any odd prime distinct from the characteristic.

#### Article information

Source
Involve, Volume 1, Number 1 (2008), 47-58.

Dates
Revised: 28 October 2007
Accepted: 28 October 2007
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.involve/1513799070

Digital Object Identifier
doi:10.2140/involve.2008.1.47

Mathematical Reviews number (MathSciNet)
MR2403066

Zentralblatt MATH identifier
1229.11139

Subjects
Primary: 11R29: Class numbers, class groups, discriminants

#### Citation

Merberg, Adam. Divisibility of class numbers of imaginary quadratic function fields. Involve 1 (2008), no. 1, 47--58. doi:10.2140/involve.2008.1.47. https://projecteuclid.org/euclid.involve/1513799070

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