Vol. 1, No. 1, 2008

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

Volume 10
Issue 5, 721–900
Issue 4, 541–720
Issue 3, 361–539
Issue 2, 181–360
Issue 1, 1–180

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
Cover Page
Editorial Board
Editors’ Addresses
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Subscriptions
Editorial Login
Author Index
Coming Soon
Contacts
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Divisibility of class numbers of imaginary quadratic function fields

Adam Merberg

Vol. 1 (2008), No. 1, 47–58
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.

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

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