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For multiplicative characters $\\chi_1,\\dots, \\chi_m$ of $\\mathbf{F}_q^\\times$, we let $J(\\chi_1,\\dots, \\chi_m)$ denote the Jacobi sum. Nicholas Katz and Zhiyong Zheng showed that for $m=2$, the normalized Jacobi sum $q^{-1/2}J(\\chi_1,\\chi_2)$ ($\\chi_1\\chi_2$ nontrivial) is asymptotically equidistributed on the unit circle as $q\\to \\infty$, when $\\chi_1$ and $\\chi_2$ run through all nontrivial multiplicative characters of $\\mathbf{F}_q^\\times$. In this paper, we show a similar property for $m\\ge 2$. 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