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Extreme value laws for intrinsic Diophantine approximation on spheres
Abstract
We study intrinsic Diophantine approximation on the sphere Sd, measured by the quality of the best rational approximation available at a given height. We show that, for d≥ 3 and along sufficiently sparse sequences of heights, these quantities have a Weibull limit distribution and the associated counting functions are asymptotically Poissonian.
Related
- Metric Diophantine approximation on planar and Veronese curves
- Diophantine approximation by primes and Landau--Siegel zeros
- On a Notion of Density Related to Restricted Diophantine Approximation
- Twisted Diophantine Approximation I: Asymptotic Theory
- Non-degeneracy and Fibering with Applications to Diophantine Approximation
BibTeX
@misc{gorodnik2026extreme,
title = {{Extreme value laws for intrinsic Diophantine approximation on spheres}},
author = {Alexander Gorodnik and Zouhair Ouaggag},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21036},
eprint = {2609.21036},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21036},
}
RIS
TY - UNPB
TI - Extreme value laws for intrinsic Diophantine approximation on spheres
AU - Alexander Gorodnik
AU - Zouhair Ouaggag
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.21036
UR - https://arxiv.org/abs/2609.21036
AB - We study intrinsic Diophantine approximation on the sphere S^d, measured by the quality of the best rational approximation available at a given height. We show that, for d≥ 3 and along sufficiently sparse sequences of heights, these quantities have a Weibull limit distribution and the associated counting functions are asymptotically Poissonian.
ER -