# Math Help - Characteristic Function of a Multivariate Cauchy

1. ## Characteristic Function of a Multivariate Cauchy

Hello, I am very lost with the following problem, is there a neat way of doing it, or just solving integral after integral is the way to go?
Any hint would be greatly appreciated.

Let $X \sim N_p(0,\Sigma)$ be independent of $Z \sim N(0,1)$. Show that $Y=X/Z$ has characteristic function

$\varphi_Y(t) = \exp\{-(t^T \Sigma t)^{1/2}\}$