Archiv der Mathematik

, Volume 99, Issue 4, pp 345–351

On the distribution of solutions to polynomial congruences

Article

DOI: 10.1007/s00013-012-0436-5

Cite this article as:
Shparlinski, I.E. Arch. Math. (2012) 99: 345. doi:10.1007/s00013-012-0436-5

Abstract

We use a result of É. Fouvry about the distribution of solutions to systems of congruences with multivariate polynomials in small cubic boxes and some ideas of W. Schmidt to derive an asymptotic formula for the number of such solutions in very general domains.

Mathematics Subject Classification (2010)

Primary 11D79Secondary 11K38

Keywords

Multivariate congruencesPolynomialsDistribution of pointsWell-shaped domains

Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.Department of ComputingMacquarie UniversitySydneyAustralia