Elementary Proofs of Representation by Ternary Quadratic Forms

TL;DR

This paper extends techniques used in classical and recent proofs to analyze which integers are represented by certain ternary quadratic forms, broadening understanding of their representational properties.

Contribution

It generalizes existing methods to four new ternary quadratic forms, expanding the classification of integers they can represent.

Findings

Extended techniques to four additional forms.

Characterized integers represented by these forms.

Enhanced understanding of ternary quadratic form representations.

Abstract

Mordell in 1958 gave a new proof of the three squares theorem. Those techniques were generalized by Blackwell, et al., in 2016 to characterize the integers represented by the remaining six "Ramanujan-Dickson ternaries". We continue the generalization of these techniques to four additional forms.