Journal article

### The density of rational points on non-singular hypersurfaces, I

Abstract:

For any $n \geq 3$, let $F ∈ ℤ[X 0,⋯,Xn]$ be a form of degree $d\geq 5$ that defines a non-singular hypersurface $X ⊂ ℙ n. The main result in this paper is a proof of the fact that the number$N(F;B) of ℚ-rational points on $X$ which have height at most $B$ satisfies $N(F;B)=Od, ε,n(Bn-1+ε) for any$\varepsilon >0$. The implied constant in this estimate depends at most upon$d$,$\varepsilon$and$n\$. New estimates are also obtained for the number of representations of a positive integer a...

Publication status:
Published

### Access Document

Publisher copy:
10.1112/S0024609305018412

### Authors

More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
Volume:
38
Issue:
3
Pages:
401-410
Publication date:
2006-06-01
DOI:
EISSN:
1469-2120
ISSN:
0024-6093
Source identifiers:
24558
Language:
English
Pubs id:
pubs:24558
UUID:
uuid:6a9a8761-6907-400a-9e45-0153bc92752f
Local pid:
pubs:24558
Deposit date:
2012-12-19