A zero-density estimate for $L$-functions associated with $\mathrm{G}\mathrm{L}(3)$ Hecke--Maass cusp forms

In this paper, we establish an asymptotic formula for the twisted second moment of $L$-functions associated with Hecke–Maass cusp forms for $\mathrm{S}\mathrm{L}(3,\mathbb{Z})$, and further deduce a weighted zero-density estimate for these $L$-functions in the spectral aspect which may have important applications in other problems.