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Norms on wedge products

🔗Gene Ward Smith <gwsmith@svpal.org>

1/10/2004 11:56:40 AM

We have a basis for these in terms of m-fold wedge products of p-adic
valuations; so a coordinate will look like

c vp1^vp2^...^vpm

for some subset of m primes in our limit, arranged in increasing order.

We get a norm consistent with the Tenney norm by taking the maximum of
the quantities

| c / (log2(p1) * log2(p2) ... log2(pm)) |

So, for instance, if <<w1 w2 w3 w4 w5 w6|| is a 7-limit wedgie, the
norm for it would be

|| <<w1 w2 w3 w4 w5 w6|| || = Max(|w1/q3}, |w2/q5|, |w3/q7|,
|w4/(q3 * q5)|, |w5/(q3 * q7)|, |w6/(q5 * q7)|)

where q3=log2(3), etc.