English

On Solutions to Some Polynomial Congruences in Small Boxes

Number Theory 2019-02-20 v1

Abstract

We use bounds of mixed character sum to study the distribution of solutions to certain polynomial systems of congruences modulo a prime pp. In particular, we obtain nontrivial results about the number of solution in boxes with the side length below p1/2p^{1/2}, which seems to be the limit of more general methods based on the bounds of exponential sums along varieties.

Keywords

Cite

@article{arxiv.1301.1758,
  title  = {On Solutions to Some Polynomial Congruences in Small Boxes},
  author = {Igor E. Shparlinski},
  journal= {arXiv preprint arXiv:1301.1758},
  year   = {2019}
}
R2 v1 2026-06-21T23:06:24.185Z