1
vote
1answer
30 views

Rescaling of Ternary quadratic forms

I was reading about the Hilbert residue symbol, and the discussion of it starts out with the assumption that we can reformat any ternary quadratic form over the integers into the form ...
1
vote
1answer
114 views

Quadratic form over the dyadic numbers

I would like to know whether $q=\langle 3,3,11\rangle$ (a diagonal ternary form) represents $2$ over $\mathbb{Q}_2$ (i.e. whether there exist $x,y,z\in\mathbb{Q}_2^\times$ such that $q(x,y,z)=2$). I ...
3
votes
2answers
316 views

Isotropy over $p$-adic numbers

Over what $p$-adic fields $\mathbb{Q}_p$ is the form $\langle3, 7, -15\rangle$ isotropic?
3
votes
2answers
231 views

Hilbert Symbols when $K =$ the $p$-adic numbers

How can I show that the Hilbert Symbol is bimultiplicative, when the local field is the $p$-adic numbers? Everything I can find just sort of asserts bimultiplicativity without much proof, so I'm ...