Minkowski's bound

Let be the ring of integers of a number field . Then any ideal contains a nonzero element such that

where Minkowski's bound depends only on and is given by

where

Proof sketch

#missing/proof

We apply Minkowski's convex body theorem to the convex symmetric compact region

which looks like

in the complex case.

#state/develop | #lang/en | #SemBr

Footnotes