A Relation between the Zeros of Different Two L-functions Which Have the Euler Product and Functional Equation

As automorphic L-functions or Artin L-functions, several classes of Lfunctions 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 zetafunction 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 RankinSelberg L-functions attached to two elliptic modular forms.