A probability distribution whose its characteristics function has finite of zeros on R Can someone give a probability distribution whose its characteristics function has finite (but at least one zeros) of zeros on the real line? All probability distributions that I has known just occur two situations: non zeros (e.g., normal distributions) and infinitely many zeros (e.g., uniform distirbutions).

The Cauchy distribution with location parameter $\mu$ and scale $\theta$ has PDF $\frac{1}{\pi \theta \left( 1 + \left( \frac{x-\mu}{\theta} \right)^2 \right)}$ (in the variable $x$) and characteristic function $\mathrm{e}^{\mathrm{i} \mu t - \theta |t|}$ (in the variable $t$).  Since $\mathrm{e}^z \neq 0$ for every $z \in \mathbb{C}$, this characteristic function has zero zeroes on the real axis (or anywhere else).  Zero is of course finite.
