29 Aug
2018
29 Aug
'18
1:48 p.m.
With "rational arguments" — not sure I know what that means. Eisenstein integers should be the ring Z[w] where w = -1/2 + i*sqrt(3/4). Since Z[w] = {K + L*w | K, L in Z} we can compute |K + L*w|^2 = (K - L/2)^2 + (3/4)*L^2 = K^2 - KL + L^2 (which is what I remembered). I'm still in the dark over what rational arguments are, and how K^2 - KL + L^2 squares with what Adam wrote. —Dan Adam Goucher wrote: ----- They're precisely the norms of Eisenstein integers with rational arguments. Wouter Meeussen wrote: -----
do they occur anywhere naturally? in combinatorics or in number theory? I bumped into them by accident looking at bracelet-stuff.
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