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Quadratic forms with p-adic coefficient

  1. Jul 15, 2010 #1
    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?
  2. jcsd
  3. Jul 16, 2010 #2


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    Gold Member

    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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