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Minkowski's bound

{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 $(r_1,r_2)$.

Minkowski lower bound for a number-field discriminant

Coprime discriminants imply linear disjointness

Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 74 / 5 / ii / Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 123 / 4 / i / Solution

Minkowski lower bound for a number-field discriminant

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Minkowski lower bound for a number-field discriminant

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