ON SIGNS OF FOURIER COEFFICIENTS OF HECKE-MAASS CUSP FORMS ON GL3

We consider sign changes of Fourier coefficients of Hecke-Maass cusp forms for the group SL3(Z). When the underlying form is self-dual, we show that there are >& epsilon; X5/6-& epsilon; sign changes among the coefficients {A(m, 1)}m & LE;X and that there is a positive proportion of sign changes for many self-dual forms. Similar result concerning the positive proportion of sign changes also hold for the real-valued coefficients A(m, m) for generic GL3 cusp forms, a result which is based on a new effective Sato-Tate type theorem for a family of GL3 cusp forms we establish. In addition, non-vanishing of the Fourier coefficients is studied under the Ramanujan-Petersson conjecture.