Class number problem for imaginary cyclic number fields

[摘要] Let N be an imaginary cyclic number field of degree 2n. When n=3 or n=2(m) greater than or equal to 2, the fields iv with class numbers equal to their genus class numbers and the fields iv with relative class numbers less than or equal to 4 are completely determined [10, 13, 26, 27]. Now assume that n greater than or equal to 5 and n is not a 2-power. Tn this paper, first we determine all imaginary cyclic number fields of degree 2n with relative class numbers less than or equal to 4. Second, we determine all imaginary cyclic number fields of degree 2n With class numbers equal to their genus class numbers. (C) 1998 Academic Press.

[发布日期] 1998-12-01