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Counting rational points on hypersurfaces

Abstract:
For any n ≧ 2, let F ε ℤ[x1, . . . , xn] be a form of degree d ≧ 2, which produces a geometrically irreducible hypersurface in ℙn-1. This paper is concerned with the number N(F;B) of rational points on F = 0 which have height at most B. For any ε > 0 we establish the estimate N(F;B) = O(Bn-2+ε), whenever either n ≦ 5 or the hypersurface is not a union of lines. Here the implied constant depends at most upon d, n and ε. © Walter de Gruyter 2005.
Publication status:
Published

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
Volume:
584
Issue:
584
Pages:
83-115
Publication date:
2005-01-01
DOI:
EISSN:
1435-5345
ISSN:
0075-4102
URN:
uuid:42199398-94c0-464d-8898-3903623cae11
Source identifiers:
25901
Local pid:
pubs:25901
Language:
English

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