Class numbers of some abelian extensions of rational function fields

Abstract

Let P be a monic irreducible polynomial. In this paper we generalize the determinant formula for h(K Pn) of Bae and Kang and the formula for h−(KPn ) of Jung and Ahn to any subfields K of the cyclotomic function field KPn . By using these formulas, we calculate the class numbers h −(K), h(K+) of all subfields K of KP when q and deg(P ) are small.

DOI: 10.1090/S0025-5718-03-01528-X

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Cite this paper

@article{Bae2004ClassNO, title={Class numbers of some abelian extensions of rational function fields}, author={Sunghan Bae and Hwanyup Jung and Jaehyun Ahn}, journal={Math. Comput.}, year={2004}, volume={73}, pages={377-386} }