  In a previous paper [KT] we introduced determinant of the Riemann operator on
Quillen's higher $K$-groups of the integer ring of an algebraic number field
$K$. We showed that the determinant expresses essentially the inverse of the so
called gamma factor of Dedekind zeta function of $K$.
  Here we study the periodicity of determinant. This comes from the famous
"periodicity" of higher $K$ groups. This periodicity is analogous to Euler's
periodicity of gamma function $\Gamma(x+1)=x\Gamma(x)$. We investigate the
"reflection formula" corresponding to Euler's reflection formula
$\Gamma(x)\Gamma(1-x)=\frac{\pi}{\sin(\pi x)}$ also.
