On the convex hull of the points on multivariate modular hyperbolas

Given integers a, m≥1 with gcd⁡(a,m)=1 and s≥2, let Hs(a,m) be the following set of integral pointsHs(a,m)={(x1,…,xs)∈Zs:x1…xs≡a(modm),={(x1,…,xs)∈Zs:1≤x1,…,xs≤m−1}. We obtain upper bounds on the number of vertices of the convex hull of Hs(a,m). These bounds generalise those known for s=2, although our approach is different.