SOLUTIONS TO POLYNOMIAL CONGRUENCES IN WELL-SHAPED SETS

作者：Kerr Bryce^*

来源：Bulletin of the Australian Mathematical Society, 2013, 88(3): 435-447.

DOI：10.1017/S0004972713000324

• polynomial congruences
• distribution of points

We use a generalisation of Vinogradov%26apos;s mean value theorem of Parsell et al. [%26apos;Near-optimal mean value estimates for multidimensional Weyl sums%26apos;, arXiv:1205.6331] and ideas of Schmidt [%26apos;Irregularities of distribution. IX%26apos;, 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.

• 出版日期2013-12