Article

Archiv der Mathematik

, Volume 99, Issue 4, pp 345-351

On the distribution of solutions to polynomial congruences

  • Igor E. ShparlinskiAffiliated withDepartment of Computing, Macquarie University Email author 

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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 11D79 Secondary 11K38

Keywords

Multivariate congruences Polynomials Distribution of points Well-shaped domains