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RATIONAL POINTS ON CUBIC HYPERSURFACES THAT SPLIT INTO FOUR FORMS

Part of: Arithmetic problems. Diophantine geometry Additive number theory; partitions Diophantine equations Forms and linear algebraic groups

Published online by Cambridge University Press:  29 January 2016

Boqing Xue  and
Lilu Zhao
Boqing Xue
Affiliation:
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China email boqing_xue@hotmail.com
Lilu Zhao
Affiliation:
School of Mathematics, Hefei University of Technology, Hefei 230009, China email zhaolilu@gmail.com

Abstract

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Let $C\in \mathbb{Z}[x_{1},\ldots ,x_{n}]$ be a cubic form. Assume that $C$ splits into four forms. Then $C(x_{1},\ldots ,x_{n})=0$ has a non-trivial integer solution provided that $n\geqslant 10$ .

MSC classification

Primary: 11D72: Equations in many variables
Secondary: 11E76: Forms of degree higher than two 11P55: Applications of the Hardy-Littlewood method 14G25: Global ground fields

Information

Type
Research Article
Information
Mathematika , Volume 62 , Issue 2 , 2016 , pp. 430 - 440
Copyright
Copyright © University College London 2016 

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