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A Lower Bound on the Number of Cyclic Function Fields With Class Number Divisible by $n$ |
Canad. Math. Bull. 49(2006), 448-463
Published:2006-09-01
Printed: Sep 2006
Printed: Sep 2006
- Allison M. Pacelli
Abstract
In this paper, we find a lower bound on the number of cyclic function
fields of prime degree~$l$ whose class numbers are divisible by a
given
integer $n$. This generalizes a previous result of D. Cardon and R.
Murty
which gives a lower bound on the number of quadratic function fields
with
class numbers divisible by $n$.
| MSC Classifications: |
11R29 - Class numbers, class groups, discriminants 11R58 - Arithmetic theory of algebraic function fields [See also 14-XX] |