Abstract

Cyclotomic function fields was introduced and used by D. Hayes [15] in 1974 to construct the maximal abelian extension of rational function fields $F_q(T)$. Since then many basic properties on cyclotomic fields have been researched by S. Galovich and M. Rosen [9, 10], D. Goss [13, 14], etc. In this paper we survey several results on class number and cyclotomic units of cyclotomic function fields.

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