Distribution of units of a cubic field with negative discriminant

[摘要] Let F be a cubic number field with negative discriminant. Taking into account the extension degree of the ray class field modulo a prime ideal, we study the residual index I(p) of residue classes represented by units in the multiplicative group of the residue field modulo a prime ideal p. The possible minimal value l(p) is given, and we give the density of prime ideals p with I(p) = l(p) if the degree of p is one, and a conjecture if the degree is 2 or 3. (C) 2001 Elsevier Science.

[发布日期] 2001-12-01