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We prove a full global Jacquet–Langlands correspondence between   $GL(n)$   and division algebras over global fields of non-zero characteristic. If   $D$   is a central division algebra of dimension   $n^2$   over a global field   $F$   of non-zero characteristic, we prove that there exists an injective map from the set of automorphic representations of   $D^{\times}$   to the set of automorphic square integrable representations of   $GL_n(F)$  , compatible at all places with the local Jacquet–Langlands correspondence for unitary representations. We characterize the image of the map. As a consequence we get multiplicity one and strong multiplicity one theorems for   $D^{\times}$  .

Global Jacquet-Langlands Correspondence for Division Algebras in Characteristic $p$