A relation between the zeros of different two $L$-functions which have the Euler product and functional equation

Details A relation between the zeros of different two $L$-functions which have the Euler product and functional equation A relation between the zeros of different two $L$-functions which have the Euler product and functional equation

2004-12-11

arxiv.org/abs/math/0412224v1

Mathematics

Number Theory

29 pages

Scientific paper

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.

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