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arXiv · 1108.5687

Binary Quadratic Forms and Counterexamples to Hasse's Local-Global Principle

Franz Lemmermeyer
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Abstract

After a brief introduction to the classical theory of binary quadratic forms we use these results for proving (most of) the claims made by Pépin in a series of articles on unsolvable quartic diophantine equations, and for constructing families of counterexamples to the Hasse Principle for curves of genus 1 defined by equations of the form $ax^4 + by^4 = z^2$.

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Franz Lemmermeyer. 2011-08-29. Binary Quadratic Forms and Counterexamples to Hasse's Local-Global Principle. https://arxiv.org/abs/1108.5687

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