# Ranicki symmetric L-groups of finite fields?

Can anyone tell me what the Ranicki symmetric L-groups $L^*(F)$ are when $F$ is a finite field? (and maybe provide a reference?) Thanks!

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This is a question which interests me a lot! –  Daniel Moskovich Dec 5 '10 at 0:17
Hi Greg, i retagged this to what I thought you meant. As it stood, this question seemed to be the only one with those tags. –  Sean Tilson Dec 5 '10 at 1:35
thanks. I had a feeling I bungled that. –  Greg Friedman Dec 5 '10 at 19:41

The symmetric $L$-group $L^*(F)$ of a field $F$ are 4-periodic, $$L^n(F)=L^{n+4}(F)$$ by Proposition 7.1 of http://www.maths.ed.ac.uk/~aar/papers/ats1.pdf
$L^{2i}(F)$ is the Witt group of $(-)^i$-symmetric forms: see Milnor and Husemoller!
$L^{2i+1}(F)=0$, see http://www.maths.ed.ac.uk/~aar/papers/simple.pdf (my shortest paper).