Geodesic
Five regular or nearly-regular ternary quadratic forms
Acta Arithmetica, Tome 77 (1996) no. 4, pp. 361-367.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

1. Introduction. In a recent article [6], the positive definite ternary quadratic forms that can possibly represent all odd positive integers were found. There are only twenty-three such forms (up to equivalence). Of these, the first nineteen were proven to represent all odd numbers. The next four are listed as "candidates". The aim of the present paper is to show that one of the candidate forms h = x² + 3y² + 11z² + xy + 7yz does represent all odd (positive) integers, and that it is regular in the sense of Dickson. We will consider a few other forms, including one in the same genus as h that is a "near miss", i.e. it fails to represent only a single number which it is eligible to represent. Our methods are similar to those in [4]. A more recent article with a short history and bibliography of work on regular ternary forms is [3].
DOI : 10.4064/aa-77-4-361-367

William Jagy 1

1 
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William Jagy. Five regular or nearly-regular ternary quadratic forms. Acta Arithmetica, Tome 77 (1996) no. 4, pp. 361-367. doi : 10.4064/aa-77-4-361-367. http://geodesic.mathdoc.fr/articles/10.4064/aa-77-4-361-367/

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