Upper bounds of some special zeros for the Rankin-Selberg L-function

Abstract

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.