Representation of Integers by Ternary Quadratic Forms: A Geometric Approach

Abstract

In 1957 N.C. Ankeny provided a new proof of the three squares theorem using geometry of numbers. This paper generalizes Ankeny's technique, proving exactly which integers are represented by $x^2+2y^2+2z^2$ and $x^2+y^2+2z^2$ as well as proving sufficient conditions for an integer to be represented by $x^2+y^2+3z^2$ and $x^2+y^2+7z^2$.

14 pages