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

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

2011-08-29

arxiv.org/abs/1108.5687v1

Mathematics

Number Theory

Scientific paper

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 $ax^4 + by^4 = z^2$.

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