Résume | $F$ is a non-Archimedean local field and $n$ a positive integer. Let $\sigma$ be an irreducible, $n$-dimensional representation of the Weil group of $F$. Using an explicit method, we attach to $\sigma$ an irreducible cuspidal representation $N(\sigma)$ of $GL(n,F)$. The main result compares $N(\sigma)$ with the representation $L(\sigma)$ attached to $\sigma$ by the Langlands correspondence. The difference between $N(\sigma)$ and $L(\sigma)$ is, in a certain sense, uniform. This reveals some interesting arithmetic properties of the Langlands correspondence. |