Some arithmetical properties of quadratic polynomials

Abstract

The problems discussed in this thesis arise in the geometry of numbers, a part of the theory of numbers which originated under the inspiration of Minkowski at the turn of the last century. The first chapter is introductory and provides the background to the main part of the thesis. The well known theorems which are needed later are stated without proofs, references being given in the appendix. In each of the remaining three chapters a different problem is considered and is preceded by a short summary. The theorems are numbered according to the chapter in which they occur.