The Hilbert symbol (after David Hilbert ) is a short form that is used in algebraic number theory . For a local field with the multiplicative group it is defined as the following figure:
A solution is called trivial if the following applies.
properties
- An element in is a square if and only if applies to all .
- For those in the following applies: .
- For those in the following applies: .
- For all in with valid .
literature
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