On an unconditional $\mathrm{G}{\mathrm{L}}_3$ analog of Selberg's result

Let $F$ be a Hecke–Maass cusp form for ${\mathrm{S}\mathrm{L}}_3(\mathbb{Z})$ with the Langlands parameter ${\mu }_F=({\mu }_{F,1},{\mu }_{F,2},{\mu }_{F,3})$ and the associated $L$-function $L(s,F)$. Define $S_F(t)={\pi }^{-1}\arg L(1\mathrm{/}2+\mathrm{i}t,F)$. When ${\mu }_F$ is in generic position, we establish an unconditional asymptotic formula for the moments of $S_F(t)$. Previously, such a formula was only known to hold under the Generalized Riemann Hypothesis. The key ingredient is a weighted zero-density estimate in the spectral aspect for $L(s,F)$, which has recently been proved by Sun and Wang in arXiv:2412.02416.