An "Anti-Hasse Principle" for Prime Twists

Details An "Anti-Hasse Principle" for Prime Twists An "Anti-Hasse Principle" for Prime Twists

2006-09-16

arxiv.org/abs/math/0609465v1

Mathematics

Number Theory

9 pages

Scientific paper

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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