What is Characteristic function?

The characteristic function of a random variable $X$ is $\varphi_X(u) = \E[e^{\iu uX}]$, $u \in \R$; of a random vector, $\varphi_X(u) = \E[e^{\iu u^\top X}]$, $u \in \R^d$. It exists for every law, determines it, and turns sums of independent variables into products.