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We consider sign changes of Fourier coefficients of Hecke-Maass cusp formsfor the group $\mathrm{SL}_3(\mathbb Z)$. When the underlying form isself-dual, we show that there are $\gg_\varepsilon X^{5/6-\varepsilon}$ signchanges among the coefficients $\{A(m,1)\}_{m\leq X}$ and that there is apositive proportion of sign changes for many self-dual forms. Similar resultconcerning the positive proportion of sign changes also hold for thereal-valued coefficients $A(m,m)$ for generic $\mathrm{GL}_3$ cusp forms, aresult which is based on a new effective Sato-Tate type theorem for a family of$\mathrm{GL}_3$ cusp forms we establish. In addition, non-vanishing of theFourier coefficients is studied under the Ramanujan-Petersson conjecture.

On Signs of Fourier Coefficients of Hecke-Maass Cusp Forms on $\mathrm{GL}_3$