The Distribution of Rational Points on Conics
D.R. Heath-Brown
TL;DR
This paper investigates how the distribution of rational points on conic sections begins to follow an asymptotic pattern, with the starting point depending on the smallest zero of the conic.
Contribution
It provides a detailed analysis of the asymptotic behavior of rational points on conics and relates it to the size of the smallest zero.
Findings
Asymptotic behavior depends on the smallest zero of the conic.
The counting function's starting point varies with the zero size.
Provides a new perspective on rational point distribution on conics.
Abstract
We examine the counting function for rational points on conics, and show how the point where the asymptotic behaviour begins depends on the size of the smallest zero.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Functional Equations Stability Results · Meromorphic and Entire Functions