A zero-density estimate for $L$-functions associated with $\mathrm{GL}(3)$ 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 $\mathrm{SL}(3,\mathbb{Z})$, and further deduce a weighted zero-density estimate for these $L$-functions in the spectral aspect which may have important applications in other problems.

33 pages. Comments welcome! arXiv admin note: text overlap with arXiv:1704.00314 by other authors