Could you suggest me a reference where the following non-holomorphic generalization of the Eisenstein series is discussed?

$$ G_{k,l}(\tau,z) = \sum_{m,n} (z+m+n\tau)^{-k}(\bar z+m+n\bar \tau)^{-l} $$

When $l=0$ and $z=0$ (and removing the sum on $(m,n)=(0,0)$) it's the standard Eisenstein series.