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A positive proportion of locally soluble quartic Thue equations are globally insoluble
Published online by Cambridge University Press: 05 August 2021
Abstract
For any fixed nonzero integer h, we show that a positive proportion of integral binary quartic forms F do locally everywhere represent h, but do not globally represent h. We order classes of integral binary quartic forms by the two generators of their ring of ${\rm GL}_{2}({\mathbb Z})$ -invariants, classically denoted by I and J.
MSC classification
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 173 , Issue 2 , September 2022 , pp. 333 - 348
- Copyright
- © The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society
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