Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Number Theory

arXiv:1805.03920 (math)
[Submitted on 10 May 2018 (v1), last revised 7 May 2019 (this version, v2)]

Title:Approximation diophantienne et distribution locale sur une surface torique II

Authors:Zhizhong Huang
View PDF
Abstract:We propose an empirical formula for the problem of local distribution of rational points of bounded height. This is a local version of the Batyrev-Manin-Peyre principle. We verify this for a toric surface, on which cuspidal rational curves and nodal rational curves all give the best approximations outside a Zariski closed subset. We prove the existence of a limit measure as well as an asymptotic formula for the critical zoom by removing a thin set.
Comments: Revised and shortened this http URL French. Some material will appear in subsequent work. To appear in Bulletin de la Société mathématique de France. Comments still welcome!
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
MSC classes: 11G50, 11K60, 14M25
Cite as: arXiv:1805.03920 [math.NT]
  (or arXiv:1805.03920v2 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1805.03920
Journal reference: Bulletin de la Société mathématique de France 148 (2), 2020, 189-235
Related DOI: https://doi.org/10.24033/bsmf.2803

Submission history

From: Zhizhong Huang [view email]
[v1] Thu, 10 May 2018 10:30:08 UTC (62 KB)
[v2] Tue, 7 May 2019 13:36:55 UTC (77 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.NT
< prev   |   next >
new | recent | 2018-05
Change to browse by:
math
math.AG

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)