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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...

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Publication status:
Published

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Publisher copy:
10.1112/S0024609305018412

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
Volume:
38
Issue:
3
Pages:
401-410
Publication date:
2006-06-05
DOI:
EISSN:
1469-2120
ISSN:
0024-6093
URN:
uuid:6a9a8761-6907-400a-9e45-0153bc92752f
Source identifiers:
24558
Local pid:
pubs:24558
Language:
English

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