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

Publication date: 29 August 2011

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 P'epin 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

a x^{4} + b y^{4} = z^{2}

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