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Results tagged with quadratic-forms
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user 1149
Algebraic and geometric theory of quadratic forms and symmetric bilinear forms, e.g., values attained by quadratic forms, isotropic subspaces, the Witt ring, invariants of quadratic forms, the discriminant and Clifford algebra of a quadratic form, Pfister forms, automorphisms of quadratic forms.
4
votes
Accepted
Verifying my other example in the Geometry of Numbers and Quadratic Forms
It's strange that I didn't see this question before, since Will and I have started thinking about these issues off-site. Anyway, recently I found (in the sense of located, not discovered) the answer …
- 65.4k
3
votes
Class number for binary quadratic forms discriminant $\Delta$ to class number $\mathbb Q(\sq...
I have always been fuzzier on the theory of indefinite binary forms than the definite theory. This may come from the fact that I got to learn the definite theory by teaching a course out of Cox's boo …
- 65.4k
22
votes
Accepted
Is -1 a sum of 2 squares in a certain field K?
This is a special case of a theorem of A. Pfister. It is well known to quadratic forms specialists. See e.g. Theorem XI.2.6 in T.Y. Lam's Introduction to Quadratic Forms over Fields.
I believe th …
- 65.4k
3
votes
Accepted
Non-representability by a binary quadratic form
Take $K = k((t))$ (formal Laurent series field) and apply Proposition V.2.3 of Serre's Local Fields to the unramified quadratic extension $Kl/K$. (Note that separability of $l/k$ is needed so that $K …