Open Access
2013 Weak approximation for cubic hypersurfaces of large dimension
Mike Swarbrick Jones
Algebra Number Theory 7(6): 1353-1363 (2013). DOI: 10.2140/ant.2013.7.1353


We address the problem of weak approximation for general cubic hypersurfaces defined over number fields with arbitrary singular locus. In particular, weak approximation is established for the smooth locus of projective, geometrically integral, nonconical cubic hypersurfaces of dimension at least 17. The proof utilises the Hardy–Littlewood circle method and the fibration method.


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Mike Swarbrick Jones. "Weak approximation for cubic hypersurfaces of large dimension." Algebra Number Theory 7 (6) 1353 - 1363, 2013.


Received: 25 October 2011; Revised: 24 July 2012; Accepted: 7 September 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1368.11058
MathSciNet: MR3107566
Digital Object Identifier: 10.2140/ant.2013.7.1353

Primary: 11G35
Secondary: 11D25 , 11D72 , 11P55 , 14G25

Keywords: circle method , cubic hypersurfaces , fibration method , local-global principles , many variables , weak approximation

Rights: Copyright © 2013 Mathematical Sciences Publishers

Vol.7 • No. 6 • 2013
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