抄録
If K is an algebraic number field with {r_1} real and 2{r_2} complex conjugate fields, n = {r_1} + 2{r_2} is the degree of the field, and D is absolute value of the discriminant of K, then we show
{D1/n} ≥ {(60)^{{r_1}/n}}{(22)^{2{r_2}/n}} + o(1), n → ∞
If the zeta function of K has no zeros β + iγ with β > 1/2 and 0 < \left| γ \
ight| < 3, then we show
{D1/n} ≥ {(188)^{{r_1}/n}}{(41)^{2{r_2}/n}} + o(1), n → ∞ .
