Abstract
Let $k$ be a function field over finite field $\mathbb{F}_q$ andlet $A$ be the ring consisting of elements of $k$ regular away from a fixed place $\infty$ of $k$.Let $\phi$ be a Drinfeld $A$-module over a finite field $L$.We define the Frobenius torus of $\phi$ by similar way with the case of elliptic curvesand study the structure when the rank of $\phi$ equal to $2,3$.For Drinfeld $A$-module $\phi$ over $K$ where $K/k$ is a finite separable extension,we define the $v$-adic representations of $Gal(K^s/K)$.When the rank of $\phi$ equal to $1$, we define the cyclotomic charactersand discuss the case of $sgn$-normalized rank $1$ Drinfeld moduleand the special case of Carlitz module.