Quadratic forms with p-adic coefficient

  • Thread starter antonio85
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How can I found out in which p-adic fields a quadratic form represent 0?

For example in which p-adic fields does the form 3x2+7y2-15z2 represent zero?
 

MathematicalPhysicist

Gold Member
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You need to calculate Hasse Invariant and the discriminant of this form.

After that there's a theorem that gives conditions for which this form represents zero.
I can't recall the condition but I think Hasse Invariant, should be equal
(-1,-d(f)) where d(f) is the discriminant and (,) is Hilbert Symbol, after now after I checked my notebook, yes I am correct.

****, what a memory...:surprised
 

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