Cubic forms over algebraic number fields
Published online by Cambridge University Press: 24 October 2008
Extract
Davenport has proved (3) that any cubic form in 32 or more variables with rational coefficients has a non-trivial rational zero. He has also announced that he has subsequently been able to reduce the number of variables to 29. Following the method of (3), we shall prove that any cubic form over any algebraic number field has a non-trivial zero in that field, provided that the number of variables is at least 54. The following is the precise form of our result.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 4 , October 1963 , pp. 683 - 705
- Copyright
- Copyright © Cambridge Philosophical Society 1963
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