Japanese Journal of Mathematics

, Volume 7, Issue 2, pp 235–294 | Cite as

Modular hyperbolas

Original articles

Abstract

We give a survey of a variety of recent results about the distribution and some geometric properties of points (x, y) on modular hyperbolas \({xy \equiv a\;(\mod m)}\). 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

modular hyperbola congruences exponential sums character sums 

Mathematics Subject Classification (2010)

11D79 11L07 11L40 11N69 

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© The Mathematical Society of Japan and Springer Japan 2012

Authors and Affiliations

  1. 1.Department of ComputingMacquarie UniversitySydneyAustralia

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