English

Modular Hyperbolas

Number Theory 2012-06-05 v4

Abstract

We give a survey of a variety of recent results about the distribution and some geometric properties of points (x,y)(x,y) on modular hyperbolas xya(modm)xy \equiv a \pmod m. We also outline a very diverse range of applications of such results, discuss multivariate generalisations and suggest a number of open problems of different levels of difficulty.

Keywords

Cite

@article{arxiv.1103.2879,
  title  = {Modular Hyperbolas},
  author = {Igor E. Shparlinski},
  journal= {arXiv preprint arXiv:1103.2879},
  year   = {2012}
}
R2 v1 2026-06-21T17:39:37.202Z