= Jacobi sum of finite-field characters
{c}
{title2=$J(\chi,\eta)=\sum_x\chi(x)\eta(1-x)$}
= Jacobi sums of finite-field characters
{c}
{synonym}
When $\chi,\eta,\chi\eta$ are nontrivial, changing variables in a product of <Gauss sums of finite-field characters> gives $G(\chi)G(\eta)=J(\chi,\eta)G(\chi\eta)$, hence $|J|=\sqrt q$. If at least one <character> is nontrivial and their product is trivial, or the other <character> is trivial, the absolute value is one. Thus all non-main terms in a two-character cyclotomic intersection count are $O(\sqrt q)$.
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