  Let $\mathbf{F}_q$ be a finite field of $q$ elements. We show that the
normalized Jacobi sum $q^{-(m-1)/2}J(\chi_1,\dots,\chi_m)$ ($\chi_1\dotsm
\chi_m$ nontrivial) is asymptotically equidistributed on the unit circle, when
$\chi_1\in \mathcal{A}_1,\dots, \chi_m\in \mathcal{A}_m$ run through arbitrary
sets of nontrivial multiplicative characters of $\mathbf{F}_q^\times$, if
$\#\mathcal{A}_1\ge q^{\frac{1}{2}+\epsilon}$, $\#\mathcal{A}_2 \ge (\log
q)^{\frac{1}{\delta}-1}$ for $\epsilon>\delta>0$ fixed and $q\to \infty$ or if
$\#\mathcal{A}_1\#\mathcal{A}_2/q\to \infty$. This extends previous results of
Xi, Z. Zheng, and the authors.

Number Theory