A Generalization of Mordell to Ternary Quadratic Forms

TL;DR

This paper extends Mordell's 1958 techniques to characterize integers represented by Ramanujan-Dickson ternary quadratic forms and three additional ternary forms, broadening understanding of their representational properties.

Contribution

It generalizes Mordell's methods to new classes of ternary quadratic forms, providing a comprehensive characterization of integers they represent.

Findings

Characterization of integers represented by Ramanujan-Dickson ternaries

Extension of techniques to three other ternary forms

Broader understanding of ternary quadratic form representations

Abstract

Mordell in 1958 gave a new proof of the three squares theorem. We generalize those techniques to characterize the integers represented by the remaining six "Ramanujan-Dickson ternaries" as well as three other ternary forms.