  Let $f$ a smooth function with compact support defined on
$PSL(2,\mathbb{Z}[i]) \backslash PSL(2,\mathbb{C})$, we prove a formula for the
Mellin transform of $f$, then we can define the micro-local lift
$d\epsilon_{it}$ to $SL(2,\mathbb{C})$. We calculate $(f,d\epsilon_{it})$ for
$f$ a cuspidal form and for $f$ an incomplete Eisenstein series. We also
establish asymptotic estimates when $t$ tends to $\infty$. We conjecture that a
new positive distribution $d\epsilon_{it}^F$, constructed with the Friedrichs'
symmetrization technique, satisfies the same asymptotic estimates that
$d\epsilon_{it}$. This would imply the quantum ergodicity for Eisenstein series
on $PSL(2,\mathbb{Z}[i]) \backslash PSL(2,\mathbb{C})$

Number Theory