Representation of Integers by Ternary Quadratic Forms: A Geometric Approach

Gabriel Durham

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arXiv · 1509.02590

Representation of Integers by Ternary Quadratic Forms: A Geometric Approach

Gabriel Durham

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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 $x^2 + y^2 + 7z^2$.

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Gabriel Durham. 2015-09-09. Representation of Integers by Ternary Quadratic Forms: A Geometric Approach. https://arxiv.org/abs/1509.02590

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