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p-Signature


Diagonalize a form over the rationals to

 diag[p^a·A,p^b·B,...],

where all the entries are integers and A, B, ... are relatively prime to p. Then the p-signature of the form (for p!=-1,2) is

 p^a+p^b+...+4k (mod 8),

where k is the number of antisquares. For p=-1, the p-signature is Sylvester's signature.


See also

Quadratic Form Signature

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References

Conway, J. H. "Re: Projective planes." math-fun@cs.arizona.edu posting, Aug. 20, 1996.

Referenced on Wolfram|Alpha

p-Signature

Cite this as:

Weisstein, Eric W. "p-Signature." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/p-Signature.html

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