Binary Quadratic Forms and Counterexamples to Hasse's LocalGlobal 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 $ax^4 + by^4 = z^2$.
 Publication:

arXiv eprints
 Pub Date:
 August 2011
 arXiv:
 arXiv:1108.5687
 Bibcode:
 2011arXiv1108.5687L
 Keywords:

 Mathematics  Number Theory