Hilbert symbol

Let $K$ be any local field. For any two nonzero elements $a,b\in K^{\times}$ , we define:

$(a,b):=\begin{cases}+1&\text{ if $z^{2}=ax^{2}+by^{2}$ has a nonzero solution % $(x,y,z)\neq(0,0,0)$ in $K^{3}$,}\\ -1&\text{ otherwise.}\end{cases}$

The number $(a,b)$ is called the Hilbert symbol of $a$ and $b$ in $K$ .

Title	Hilbert symbol
Canonical name	HilbertSymbol
Date of creation	2013-03-22 12:50:48
Last modified on	2013-03-22 12:50:48
Owner	djao (24)
Last modified by	djao (24)
Numerical id	5
Author	djao (24)
Entry type	Definition
Classification	msc 11S31
Classification	msc 11S80