 Imaginary quadratic Minkowski disk bound

ID: imaginary-quadratic-minkowski-disk-bound

Let

K = Q (- d)

d > 0

with

d \neq \equiv 3 (mod 4)

, so

O_{K} = Z [- d]

I

is a lattice in

C ≃ R^{2}

of covolume

d N (I)

. Applying the Minkowski convex body theorem to a disk gives a nonzero

α \in I

satisfying

0 < ∣ N_{K / Q} (α) ∣ \leq \frac{4 d}{π} N (I) .

 New to topics? Read the docs here!