Counterexamples to the Hasse principle

Wayne Aitken; Franz Lemmermeyer

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arXiv · 1108.6310

Counterexamples to the Hasse principle

Wayne Aitken·Franz Lemmermeyer

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Abstract

In this article we develop counterexamples to the Hasse principle using only techniques from undergraduate number theory and algebra. By keeping the technical prerequisites to a minimum, we hope to provide a path for nonspecialists to this interesting area of number theory. The counterexamples considered here extend the classical counterexample of Lind and Reichardt. As discussed in an appendix, this type of counterexample is important in the theory of elliptic curves: today they are interpreted as nontrivial elements in the Tate--Shafarevich group.

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Wayne Aitken, Franz Lemmermeyer. 2011-08-31. Counterexamples to the Hasse principle. https://arxiv.org/abs/1108.6310

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