Ramanujam, C. P. (1963) Cubic forms over algebraic number fields Mathematical Proceedings of the Cambridge Philosophical Society, 59 (4). pp. 683-705. ISSN 0305-0041
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Official URL: http://journals.cambridge.org/action/displayAbstra...
Related URL: http://dx.doi.org/10.1017/S0305004100003698
Abstract
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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Cambridge University Press. |
| ID Code: | 82927 |
| Deposited On: | 15 Feb 2012 12:28 |
| Last Modified: | 15 Feb 2012 12:28 |
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