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An "Anti-Hasse Principle" for Prime Twists

Pete L. Clark
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Abstract

Given an algebraic curve C/Q having points everywhere locally and endowed with a suitable involution, we show that there exists a positive density family of prime quadratic twists of C violating the Hasse principle. The result applies in particular to w_N-Atkin-Lehner twists of most modular curves X_0(N) and to w_p-Atkin-Lehner twists of certain Shimura curves X^{D+}.

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Pete L. Clark. 2006-09-16. An "Anti-Hasse Principle" for Prime Twists. https://arxiv.org/abs/math/0609465

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