Equidistribution, covering radius, and Diophantine approximation for
 rational points on the sphere

Q: What type of study is this?

This is a Quantitative Study study.

Claire Burrin; Matthias Gröbner

doi:10.48550/arxiv.2502.17678

February 24, 2025Open Access

Equidistribution, covering radius, and Diophantine approximation for rational points on the sphere

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Key Points

Improved equidistribution bounds were found for rational points on the sphere in smaller spherical caps.
Using Hecke operators, this study clarifies the relationship between equidistribution and covering radius.
The findings are linked to Diophantine approximation, enhancing understanding of Linnik's conjecture.
The implications of this research could influence future studies in number theory and geometric analysis.

Implication

This analysis reveals improved equidistribution bounds for rational points in spherical caps, indicating connections to Diophantine approximation.

Abstract

We consider rational points on the sphere and investigate their equidistribution in shrinking spherical caps. For the two-dimensional sphere, we leverage Hecke operators to obtain a significantly improved small-scale equidistribution bound, and discuss connections to the covering radius problem, intrinsic Diophantine approximation, and Linnik's conjecture on sums of two squares and a mini-square.

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Cite This Study

Burrin et al. (2025) studied this question.

synapsesocial.com/papers/68f0d5eb105731330a2b1f91 https://doi.org/10.48550/arxiv.2502.17678

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Equidistribution, covering radius, and Diophantine approximation for rational points on the sphere

Key Points

Implication

Abstract

Discussion

Cite This Study

Equidistribution, covering radius, and Diophantine approximation for rational points on the sphere

Key Points

Implication

Abstract

Discussion

Cite This Study

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