Involve: A Journal of Mathematics

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

Divisibility of class numbers of imaginary quadratic function fields

Adam Merberg

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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

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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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11R29: Class numbers, class groups, discriminants
Secondary: 11R11: Quadratic extensions

number theory quadratic function fields class numbers class groups divisibility


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.

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