Vol. 1, No. 1, 2008

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
Editors' interests
ISSN (electronic): 1944-4184
ISSN (print): 1944-4176
Author index
To appear
Other MSP journals
Divisibility of class numbers of imaginary quadratic function fields

Adam Merberg

Vol. 1 (2008), No. 1, 47–58

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.

number theory, quadratic function fields, class numbers, class groups, divisibility
Mathematical Subject Classification 2000
Primary: 11R29
Secondary: 11R11
Received: 3 August 2007
Revised: 28 October 2007
Accepted: 28 October 2007
Published: 28 February 2008

Communicated by Ken Ono
Adam Merberg
Department of Mathematics
Brown University
151 Thayer Street
Providence, RI 02912
United States