Involve: A Journal of Mathematics
- Volume 1, Number 1 (2008), 47-58.
Divisibility of class numbers of imaginary quadratic function fields
We consider applications to function fields of methods previously used to study divisibility of class numbers of quadratic number fields. Let be a quadratic extension of , where 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 whose class numbers are indivisible by any odd prime distinct from the characteristic.
Involve, Volume 1, Number 1 (2008), 47-58.
Received: 3 August 2007
Revised: 28 October 2007
Accepted: 28 October 2007
First available in Project Euclid: 20 December 2017
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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