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 H-s(a, m) be the following set of integral points H-s(a, m) = {(x(1),..., x(s)) is an element of Z(s) : x(1) ... x(s) equivalent to a (mod m), 1 <= x(1,)..., x(s) <= m - 1} We obtain upper bounds on the number of vertices of the convex hull of H-s(a, m) . These bounds generalise those known for s = 2, although our approach is different. (C) 2016 Elsevier Inc. All rights reserved.