We use a generalisation of Vinogradov's mean value theorem of Parsell et al.['Near-optimal mean value estimates for multidimensional Weyl sums', arXiv:1205.6331] and ideas of Schmidt ['Irregularities of distribution. IX', Acta Arith. 27 (1975), 385-396] to give nontrivial bounds for the number of solutions to polynomial congruences, when the solutions lie in a very general class of sets, including all convex sets.
- distribution of points
- polynomial congruences