Modular Hyperbolas

2011/03/15 by Shparlinski, Igor E. · 2 citations
#11A07 #11D79 #11K38 #11L07 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1103.2879

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 ≡ 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.

Cited by

• Spectrally indistinguishable pseudorandom graphs
• On denominators of consecutive SL(2,\mathbb N)-saturated Farey fractions

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