{ "id": "1612.01440", "version": "v1", "published": "2016-12-05T17:21:31.000Z", "updated": "2016-12-05T17:21:31.000Z", "title": "Hasse Principle Violations for Atkin-Lehner Twists of Shimura Curves", "authors": [ "Pete L. Clark", "James Stankewicz" ], "comment": "11 pages, submitted", "categories": [ "math.NT" ], "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 $\\mathbb Q$.", "revisions": [ { "version": "v1", "updated": "2016-12-05T17:21:31.000Z" } ], "analyses": { "subjects": [ "11G18", "11G30" ], "keywords": [ "hasse principle violations", "shimura curve", "atkin-lehner twists", "indefinite rational quaternion algebra", "main atkin-lehner involution" ], "note": { "typesetting": "TeX", "pages": 11, "language": "en", "license": "arXiv", "status": "editable" } } }