Approximation diophantienne et distribution locale sur une surface torique II

authored by

Zhizhong Huang

Abstract

(Diophantine approximation and local distribution on a toric surface II). - 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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

Type

Article

Journal

Bulletin de la Societe Mathematique de France

Volume

148

Pages

189-235

No. of pages

47

ISSN

0037-9484

Publication date

06.2020

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

General Mathematics

Electronic version(s)

https://doi.org/10.48550/arXiv.1805.03920 (Access: Open)
https://doi.org/10.24033/bsmf.2803 (Access: Closed)