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

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

References in corpus (2)

• Families of noncongruent numbers
• A Note on Pépin's counter examples to the Hasse principle for curves of genus 1

Cited by in corpus (1)

• Hilbert 2-Class Fields and 2-Descent