On Properties of Certain Special Zeros of Functions in the Selberg Class

Abstract

In this paper, assuming generalized Riemann hypothesis, we give an upper bound for the multiplicity of eventual zero at central point 1 / 2 and location of the first zero with positive imaginary part of function in a certain subclass of the extended Selberg class. We apply our results to automorphic L-functions attached to irreducible unitary automorphic representations of $$GL_N(\mathbb {Q})$$ .