TL;DR
This paper surveys recent research on the distribution and geometric properties of points on modular hyperbolas, exploring applications, generalizations, and open problems in the area.
Contribution
It provides a comprehensive overview of recent results, applications, and open questions related to modular hyperbolas, highlighting diverse research directions.
Findings
Distribution patterns of points on modular hyperbolas
Geometric properties of these points
Potential applications and open problems
Abstract
We give a survey of a variety of recent results about the distribution and some geometric properties of points on modular hyperbolas . 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.
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Taxonomy
TopicsAnalytic Number Theory Research · Mathematical and Theoretical Analysis · Mathematical Dynamics and Fractals