A spectral mean value theorem for GL(3)

In this paper, we will prove a spectral mean value theorem for the first Fourier coefficients of GL(3) Maass forms. It is the analogue of the local Weyl law for GL(3) proved by Lapid and Müller (2009) [LM] and the sharp upper bound in the global Weyl law for GL(3) proved by Donnelly (1982) [Do], Miller (2001) [Mi], Müller (2007) [Mu], Lindenstrauss and Venkatesh (2007) [LV], Lapid and Müller (2009) [LM], etc.