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Counting rational points on smooth cyclic covers

Abstract:
A conjecture of Serre concerns the number of rational points of bounded height on a finite cover of projective space Pn-1. In this paper, we achieve Serre's conjecture in the special case of smooth cyclic covers of any degree when n≥ 10, and surpass it for covers of degree r≥ 3 when n> 10. This is achieved by a new bound for the number of perfect r-th power values of a polynomial with nonsingular leading form, obtained via a combination of an r-th power sieve and the q-analogue of van der Corput's method. © 2012 Elsevier Inc.
Publication status:
Published

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Publisher copy:
10.1016/j.jnt.2012.02.010

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Pierce, LB More by this author
Journal:
JOURNAL OF NUMBER THEORY
Volume:
132
Issue:
8
Pages:
1741-1757
Publication date:
2012-08-05
DOI:
ISSN:
0022-314X
URN:
uuid:e46c888c-39d4-46dc-b672-fe0c1367269c
Source identifiers:
329388
Local pid:
pubs:329388

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