In this paper, we prove some conditional results about the order of zero at central point s = 1/2 of the Rankin-Selberg L-function L(s, πf × π͠′f). Then, we give an upper bound for the height of the first zero with positive imaginary part of L(s, πf × π͠′f). We apply our results to automorphic L-functions.

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In this article we establish the zero-free region of certain Dirichlet polynomials LF,X arising in approximate functional equation for functions in the Selberg class and we prove an asymptotic formula for the number of zeros of LF,X .

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