  There is a well-known zeta function of the $\mathbb{Z}$-dynamical system
generated by an element of the symmetric group. By considering this zeta
function as a model, we can construct a new zeta function of an element of the
braid group.In this paper,we show that the Alexander polynomial which is the
most classical polynomial invariant of knots can be expressed in terms of this
braid zeta function.Furthermore we define the function $Z_q$ associated with
some braids. We show that this function can be expressed by some braid zeta
function for the case of special braids whose closures are isotopic to certain
torus knots.
