Hilbert symbol

Let K be any local fieldMathworldPlanetmath. For any two nonzero elements a,bK×, we define:

(a,b):={+1 if z2=ax2+by2 has a nonzero solution (x,y,z)(0,0,0) in K3,-1 otherwise.

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