In Bhargava's paper "The fifteen theorem", it is mentioned and used that the genus of the ternary form X^2+2Y^2+2YZ+5Z^2 , consists of a single class. Can some one give me a reference/proof of this fact?
Try " Universal Quadratic Forms and the Fifteen Theorem " by J. H. Conway in Contemporary Mathematics.
as well as
J. H. Conway, The sensual (quadratic) form, Carus Mathematical Monographs 26,
MAA, 1997.
[J H. Conway and N. A. Sloane, Sphere packings, lattices and groups, Grundlehren der Mathematischen Wissenschaften 290, Springer-Verlag, New York, 1999.
I do not find it in any of the references given above. Besides, there is hardly any proof in the above references. Perhaps one has to write down all reduced positive definite ternary forms of discriminant 9 in the sense of Minkowski or Eisenstein and see if any of them is in the same genus and then try to prove they are isomorphic.
- Badges
- Science topic
- Similar topics
- Mathematical Sciences
- Algebra