Hasse Principle Violations for Atkin-Lehner Twists of Shimura Curves

2016/12/05 by Clark, Pete L., Stankewicz, James
#11G18 #11G30 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1612.01440

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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