  We consider a variant expression to regularize the Euler product
representation of the zeta functions, where we mainly apply to that of the
Riemann zeta function in this paper. The regularization itself is identical to
that of the zeta function of the summation expression, but the non-use of the
M\"oebius function enable us to confirm a finite behavior of residual terms
which means an absence of zeros except for the critical line. Same technique
can be applied to the $L$-function associated to the elliptic curve, and we can
deal with the Taylor expansion at the pole in critical strip which is deeply
related to the Birch--Swinnerton-Dyer conjecture.
