Representation of Integers by Ternary Quadratic Forms: A Geometric\n Approach

2015/09/08 by Gabriel Durham, Durham, Gabriel
Computer Science · Mathematics · #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Number Theory (math.NT) #Numerical Methods and Algorithms

paper · pdf · doi:10.48550/arxiv.1509.02590

openalex publication_date 2015/09/08 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

In 1957 N.C. Ankeny provided a new proof of the three squares theorem using\ngeometry of numbers. This paper generalizes Ankeny's technique, proving exactly\nwhich integers are represented by x² + 2y² + 2z² and x² + y² + 2z² as\nwell as proving sufficient conditions for an integer to be represented by\nx²+y²+3z² and x² + y² + 7z².\n

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