[math-fun] inversion in finite field ~= fourier transform?

I noticed this a few years ago and recently came across it again. In GF(2^n), inversion behaves very much like a change between conjugate observables; when you add a "delta function" h, inversion spreads it out over the whole spectrum: (x+h)^(-1) = (x+h)^(N) = sum (N choose k) x^(N-k) h^k. Is there some kind of equivalent of a gaussian that preserves form under addition and inversion? -- Mike Stay staym@clear.net.nz http://www.xaim.com/staym