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SOLUTIONS TO POLYNOMIAL CONGRUENCES IN WELL-SHAPED SETS
Published online by Cambridge University Press: 12 June 2013
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.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 88 , Issue 3 , December 2013 , pp. 435 - 447
- Copyright
- Copyright ©2013 Australian Mathematical Publishing Association Inc.
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