CYCLOTOMIC UNITS AND DIVISIBILITY OF THE CLASS NUMBER OF FUNCTION FIELDS
CYCLOTOMIC UNITS AND DIVISIBILITY OF THE CLASS NUMBER OF FUNCTION FIELDS
Let <TEX>$textsc{k}$</TEX>＝<TEX>$F_{q}$</TEX>(T) be a rational function field. Let <TEX>$\ell$</TEX> be a prime number with (<TEX>$\ell$</TEX>, q-1) ＝ 1. Let K/<TEX>$textsc{k}$</TEX> be an elmentary abelian <TEX>$\ell$</TEX>-extension which is contained in some cyclotomic function field. In this paper, we study the <TEX>$\ell$</TEX>-divisibility of ideal class number <TEX>$h_{K}$</TEX> of K by using cyclotomic …