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...
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- Publication status:
- Published
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- Publisher copy:
- 10.1112/S0024609305018412
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Bibliographic Details
- 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
Item Description
- Language:
- English
- Pubs id:
-
pubs:24558
- UUID:
-
uuid:6a9a8761-6907-400a-9e45-0153bc92752f
- Local pid:
- pubs:24558
- Deposit date:
- 2012-12-19
Terms of use
- Copyright date:
- 2006
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