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