On solutions to some polynomial congruences in small boxes

Authors

  • I. E. Shparlinksi Macquarie Univ.

Keywords:

Multivariate congruences, distribution of points

Abstract

We use bounds of mixed character sum to study the distribution of solutions to certain polynomial systems of congruences modulo a prime \(p\). In particular, we obtain nontrivial results about the number of solution in boxes with the side length below \(p^{1/2}\), which seems to be the limit of more general methods based on the bounds of exponential sums along varieties. 10.1017/S0004972713000671

Published

2014-01-27

Issue

Vol. 89 No. 2 (2014)

Section

Articles
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