Dual of the Weil norm proof: Difference between revisions
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{{ | {{Archive}} | ||
(Archived from Facebook, originally a post by [[Mike Battaglia]] addressing [[ | (Archived from Facebook, originally a post by [[Mike Battaglia]] addressing [[Gene Smith]]) | ||
OK, so I proved the conjecture. The dual to the weil norm is max(<V 0|) - min(<V 0|). I'll formulate [[monzo]]s as column vectors and [[val]]s as row vectors below. | OK, so I proved the conjecture. The dual to the weil norm is max(<V 0|) - min(<V 0|). I'll formulate [[monzo]]s as column vectors and [[val]]s as row vectors below. | ||
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Let M be the space of p-limit real monzos with the Weil norm on them. The Weil norm of a weighted monzo |a b c ...> is 1/2*(|a| + |b| + |c| + ... + |a+b+c+...|), giving you log(max(n,d)). | Let M be the space of p-limit real monzos with the Weil norm on them. The Weil norm of a weighted monzo |a b c ...> is 1/2*(|a| + |b| + |c| + ... + |a+b+c+...|), giving you log(max(n,d)). | ||
Note that this still looks like an L1 norm - in fact, it's the L1 norm of the " | Note that this still looks like an L1 norm - in fact, it's the L1 norm of the "augmented monzo" | ||
1/2 * |a b c ... ; (a+b+c+...)> | 1/2 * |a b c ... ; (a+b+c+...)> | ||
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QED. | QED. | ||
[[Category:Math]] | [[Category:Math]] | ||
[[Category:Archive]] | [[Category:Archive]] | ||