Abstract:We prove that the set of CM points on the Shimura curve associated to an Eichler order inside an indefinite quaternion Q-algebra, is in bijection with the set of certain classes of p-adic binary quadratic forms, where p is a prime dividing the discriminant of the quaternion algebra. The classes of p-adic binary quadratic forms are obtained by the action of a discrete and cocompact subgroup of PGL 2 (Q p ) arising from the p-adic uniformization of the Shimura curve. We finally compute families of p-adic binary … Show more
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