$K_{2} $ OF A FERMAT QUOTIENT AND THE VALUE OF ITS $L $ FUNCTION

$\ovalbox{\tt\small REJECT}$xa$\oplus$Hl11$\neq$bfflFRXE$\Phi$-$\beta\beta $ (KEN-ICIIIRO KIMURA) Introduction. In 1984, Beilinson[Be] formulated a beautiful conjecture which re-lates the values at each integer of Hasse-Weil $L $ functions of a proper smooth variety X over a number field to the covolume of the image of the regulator map erg: $H_{A}^{i}(X, \mathbb{Q}(j))arrow H_{\mathcal{D}}^{i}(X_{\mathbb{C}},\mathbb{R}(j))$ where $H_{A}^{i}(X, \mathbb{Q}(j))=K_{2j-i}^{\langle j)}(X)_{\mathbb{Q}} $ is called absolute cohomology group which is