The number of coefficients of automorphic L -functions for GLmGLm of same signs

Let π   be an irreducible unitary cuspidal representation for GLm(AQ)GLm(AQ), and let L(s,π)L(s,π) be the automorphic L-function attached to π  , which has a Dirichlet series expression in the half-plane ℜes>1. When π is self-contragredient, all the coefficients in the Dirichlet series expression are real. In this paper we give non-trivial lower bounds for the number of positive and negative coefficients, respectively.