Minkowski lower bound for a number-field discriminant
= Minkowski lower bound for a number-field discriminant
{c}
Since every nonzero integral ideal has norm at least one, the <Minkowski bound for ideal classes> implies
$$
|d_K|\geq
\left(\frac\pi4\right)^{2r_2}
\left(\frac{n^n}{n!}\right)^2
$$
for every number field of degree $n$ and signature $(r_1,r_2)$.