Algebraic Theory of Quadratic Numbers by Mak Trifković

Author:Mak Trifković
Language: eng
Format: epub, pdf
Publisher: Springer New York, New York, NY

5.3 Minkowski’s Theorem

The geometric fact alluded to at the end of the previous section is Minkowski’s theorem: a planar region that is sufficiently big, symmetric, and regular contains a nonzero lattice point.

5.2.1 Definition.

We say that a set is nice if it satisfies all of the following: (a) S is centrally symmetric around 0: if x ∈ S, then − x ∈ S.

(b) S is convex: the line segment joining any two points in S is entirely inside S.

(c) S is measurable: we can make sense of the integral defining the area of S.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.