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SOLUTIONS TO POLYNOMIAL CONGRUENCES IN WELL-SHAPED SETS

Part of: Probabilistic theory: distribution modulo $1$; metric theory of algorithms Diophantine equations

Published online by Cambridge University Press:  12 June 2013

BRYCE KERR
BRYCE KERR*
Affiliation:
Department of Computing, Macquarie University, Sydney, NSW 2109, Australia email bryce.kerr@students.mq.edu.au
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Abstract

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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.

Keywords

polynomial congruencesdistribution of points

MSC classification

Secondary: 11D79: Congruences in many variables 11K38: Irregularities of distribution, discrepancy
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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