Lan Nguyen

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 20, 2014, Number 5, Pages 49—57

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## Details

### Authors and affiliations

Lan Nguyen

*Department of Mathematics, University of Wisconsin-Parkside
Ann Arbor, MI 48109, United States
*

### Abstract

It is known that any binary rational cubic form satisfies the Hasse principle. The next natural question to ask is whether this still holds for a system of binary rational cubic forms. However, there seems to be no known result on this topic. In our paper we show, by establishing an explicit equivalence between a rational cubic form and an intersection of quadric surfaces, that any system of finitely many binary rational cubic forms satisfies the Hasse principle.

### Keywords

- Hasse principle
- Cubic plane curve
- Cubic form
- Quadratic form
- System of cubic forms
- System of binary quadratic forms
- Selmer curve
- Finite Basis theorem

### AMS Classification

- 11XXX

### References

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*ax*^{3}+*by*^{3}+*cz*^{3}=0, Acta Math., Vol. 85, 1951, No. 1, 203–362. - Serre, J. P., A First Course in Arithmetic, Graduate Texts in Mathematics, Vol. 7, Berlin, New York: Springer–Verlag, 1973.

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## Cite this paper

APANguyen, L. (2014). On the local and global principle for system of binary rational cubic forms. Notes on Number Theory and Discrete Mathematics, 20(5), 49-57.

ChicagoNguyen, Lan. “On the Local and Global Principle for System of Binary Rational Cubic Forms.” Notes on Number Theory and Discrete Mathematics 20, no. 5 (2014): 49-57.

MLANguyen, Lan. “On the Local and Global Principle for System of Binary Rational Cubic Forms.” Notes on Number Theory and Discrete Mathematics 20.5 (2014): 49-57. Print.