Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 435-447 |
| Number of pages | 13 |
| Journal | Bulletin of the Australian Mathematical Society |
| Volume | 88 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2013 |
Keywords
- distribution of points
- polynomial congruences