Class numbers of some abelian extensions of rational function fields

Authors:
Sunghan Bae, Hwanyup Jung and Jaehyun Ahn

Journal:
Math. Comp. **73** (2004), 377-386

MSC (2000):
Primary 11R60, 11R29

Published electronically:
April 28, 2003

MathSciNet review:
2034128

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a monic irreducible polynomial. In this paper we generalize the determinant formula for of Bae and Kang and the formula for of Jung and Ahn to any subfields of the cyclotomic function field By using these formulas, we calculate the class numbers of all subfields of when and are small.

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Additional Information

**Sunghan Bae**

Affiliation:
Department of Mathematics, KAIST, Daejon, 305-701 Korea

Email:
shbae@math.kaist.ac.kr

**Hwanyup Jung**

Affiliation:
Department of Mathematics, KAIST, Daejon, 305-701 Korea

Email:
hyjung@mathx.kaist.ac.kr

**Jaehyun Ahn**

Affiliation:
Department of Mathematics, KAIST, Daejon, 305-701 Korea

Email:
jaehyun@mathx.kaist.ac.kr

DOI:
http://dx.doi.org/10.1090/S0025-5718-03-01528-X

Keywords:
Class number,
function field

Received by editor(s):
March 27, 2002

Received by editor(s) in revised form:
May 20, 2002

Published electronically:
April 28, 2003

Article copyright:
© Copyright 2003
American Mathematical Society