On the Twisted Spectral Large Sieve Inequality for ${\mathrm{PGL}}_2(\mathbb{Z}[i])\backslash {\mathrm{PGL}}_2(\mathbb{C})$

Abstract

In this paper, we extend the twisted spectral large sieve inequalities of Deshouillers, Iwaniec, Luo, and Young from ${\mathrm{SL}}_2(\mathbb{Z})$ onto ${\mathrm{PGL}}_2(\mathbb{Z}[i])$.

24 pages