On the convex hull of solutions to polynomial congruences

Igor E. Shparlinski

doi:10.1016/j.jnt.2011.06.016

On the convex hull of solutions to polynomial congruences

Igor E. Shparlinski^*

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We give an upper bound on the number of vertices of the convex hull of the set of solutions to multivariate polynomial congruences modulo a prime p. The result is based on a combination of an estimate of G. Andrews on the number of vertices of integral polyhedra and a result of É. Fouvry about the distribution of zeros of multivariate polynomials in small boxes.

Original language	English
Pages (from-to)	254-257
Number of pages	4
Journal	Journal of Number Theory
Volume	132
Issue number	1
DOIs	https://doi.org/10.1016/j.jnt.2011.06.016
Publication status	Published - Jan 2012

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10.1016/j.jnt.2011.06.016

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AB - We give an upper bound on the number of vertices of the convex hull of the set of solutions to multivariate polynomial congruences modulo a prime p. The result is based on a combination of an estimate of G. Andrews on the number of vertices of integral polyhedra and a result of É. Fouvry about the distribution of zeros of multivariate polynomials in small boxes.

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On the convex hull of solutions to polynomial congruences

Abstract

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