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December 2020 Counterexamples to the local-global principle associated with Swinnerton-Dyer's cubic form
Yoshinosuke Hirakawa
Rocky Mountain J. Math. 50(6): 2097-2102 (December 2020). DOI: 10.1216/rmj.2020.50.2097

Abstract

We imitate a classical construction of a counterexample to the local-global principle of cubic forms of 4 variables which was discovered first by Swinnerton-Dyer (Mathematika (1962)). Our construction gives new explicit families of counterexamples in homogeneous forms of 4,5,6,,2n+2 variables of degree 2n+1 for infinitely many integers n. It is contrastive to Swinnerton-Dyer’s original construction that we do not need any concrete calculation in the proof of local solubility.

Citation

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Yoshinosuke Hirakawa. "Counterexamples to the local-global principle associated with Swinnerton-Dyer's cubic form." Rocky Mountain J. Math. 50 (6) 2097 - 2102, December 2020. https://doi.org/10.1216/rmj.2020.50.2097

Information

Received: 30 October 2019; Accepted: 30 April 2020; Published: December 2020
First available in Project Euclid: 5 January 2021

Digital Object Identifier: 10.1216/rmj.2020.50.2097

Subjects:
Primary: 11D57
Secondary: 11D41, 11D72, 11R18

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 6 • December 2020
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