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2008 Divisibility of class numbers of imaginary quadratic function fields
Adam Merberg
Involve 1(1): 47-58 (2008). DOI: 10.2140/involve.2008.1.47


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.


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Adam Merberg. "Divisibility of class numbers of imaginary quadratic function fields." Involve 1 (1) 47 - 58, 2008.


Received: 3 August 2007; Revised: 28 October 2007; Accepted: 28 October 2007; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1229.11139
MathSciNet: MR2403066
Digital Object Identifier: 10.2140/involve.2008.1.47

Primary: 11R29
Secondary: 11R11

Keywords: class groups , class numbers , divisibility , number theory , quadratic function fields

Rights: Copyright © 2008 Mathematical Sciences Publishers


Vol.1 • No. 1 • 2008
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