A zero-density estimate for $L$-functions associated with $\rm GL(3)$ Hecke--Maass cusp forms

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