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A Lower Bound on the Number of Cyclic Function Fields With Class Number Divisible by $n$

  Published:2006-09-01
 Printed: Sep 2006
  • Allison M. Pacelli
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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, 11R58 show english descriptions Class numbers, class groups, discriminants
Arithmetic theory of algebraic function fields [See also 14-XX]
11R29 - Class numbers, class groups, discriminants
11R58 - Arithmetic theory of algebraic function fields [See also 14-XX]
 

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