The following is a corollary to the famous Minkowski’s theorem on lattices and convex regions. It was also found by Minkowski and sometimes also called Minkowski’s theorem.
Theorem 1 (Minkowski’s Theorem).
The constant , as in the theorem, is usually called the Minkowski’s constant.
In the applications, one uses Stirling’s formula to find approximations of Minkowski’s constant. The following is an immediate corollary of Theorem 1.
See the entry on discriminants (http://planetmath.org/DiscriminantOfANumberField) for the relationship between and the ramification of primes.
|Date of creation||2013-03-22 15:05:33|
|Last modified on||2013-03-22 15:05:33|
|Last modified by||alozano (2414)|
|Defines||Minkowski’s theorem on ideal classes|