Solutions to polynomial congruences in well-shaped sets

Bryce Kerr

Research output: Contribution to journalArticle

8 Citations (Scopus)

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 languageEnglish
Pages (from-to)435-447
Number of pages13
JournalBulletin of the Australian Mathematical Society
Volume88
Issue number3
DOIs
Publication statusPublished - 2013

Keywords

  • distribution of points
  • polynomial congruences

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