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The density of rational points on non-singular hypersurfaces

Abstract:

Let F(x) =F[x1,...,xn]∈ℤ[x1,...,xn] be a non-singular form of degree d≥2, and let N(F, X)=#{xεℤ n ;F(x)=0, |x|≤X}, where {Mathematical expression}. It was shown by Fujiwara [4] [Upper bounds for the number of lattice points on hypersurfaces, Number theory and combinatorics, Japan, 1984, (World Scientific Publishing Co., Singapore, 1985)] that N(F, X)≪X n-2+2/n for any fixed form F. It is shown here that the exponent may be reduced to n - 2 + 2/(n + 1), for n ≥ 4, and to n - 3 + 15/(n + 5) for...

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Publisher copy:
10.1007/BF02830871

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Springer India
Journal:
Proceedings Mathematical Sciences More from this journal
Volume:
104
Issue:
1
Pages:
13-29
Publication date:
1994-02-01
DOI:
EISSN:
0973-7685
ISSN:
0253-4142
Language:
English
Keywords:
Pubs id:
pubs:9929
UUID:
uuid:684bd445-9a4e-4e61-9706-3813ad526ffe
Local pid:
pubs:9929
Source identifiers:
9929
Deposit date:
2013-02-20

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