Abstract |
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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.
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Keywords
number theory, quadratic function fields, class numbers, class groups, divisibility
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Mathematical Subject Classification
Primary: 11R29
Secondary: 11R11
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Authors
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