Details
| Original language | French |
|---|---|
| Pages (from-to) | 189-235 |
| Number of pages | 47 |
| Journal | Bulletin de la Societe Mathematique de France |
| Volume | 148 |
| Issue number | 2 |
| Publication status | Published - Jun 2020 |
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.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Bulletin de la Societe Mathematique de France, Vol. 148, No. 2, 06.2020, p. 189-235.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Approximation diophantienne et distribution locale sur une surface torique II
AU - Huang, Zhizhong
PY - 2020/6
Y1 - 2020/6
N2 - (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.
AB - (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.
UR - http://www.scopus.com/inward/record.url?scp=85091851772&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1805.03920
DO - 10.48550/arXiv.1805.03920
M3 - Article
AN - SCOPUS:85091851772
VL - 148
SP - 189
EP - 235
JO - Bulletin de la Societe Mathematique de France
JF - Bulletin de la Societe Mathematique de France
SN - 0037-9484
IS - 2
ER -