Hasse Principle Violations for Atkin-Lehner Twists of Shimura Curves

Published 5 Dec 2016 in math.NT | (1612.01440v1)

Abstract: Let $D > 546$ be the discriminant of an indefinite rational quaternion algebra. We show that there are infinitely many imaginary quadratic fields $l/\mathbb Q$ such that the twist of the Shimura curve $X^D$ by the main Atkin-Lehner involution $w_D$ and $l/\mathbb Q$ violates the Hasse Principle over $\mathbb Q$.

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