  As automorphic $L$-functions or Artin $L$-functions, several classes of
$L$-functions have Euler products and functional equations. In this paper we
study the zeros of $L$-functions which have the Euler products and functional
equations. We show that there exists some relation between the zeros of the
Riemann zeta-function and the zeros of such $L$-functions. As a special case of
our results, we find the relations between the zeros of the Riemann
zeta-function and the zeros of automorphic $L$-functions attached to elliptic
modular forms or the zeros of Rankin-Selberg $L$-functions attached to two
elliptic modular forms.
