Arithmetic Properties of the Shimura-shintani-waldspurger Correspondence
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چکیده
We prove that the theta correspondence for the dual pair (S̃L2, PB×), for B an indefinite quaternion algebra over Q, preserves rationality and p-integrality in both directions. As a consequence, we deduce the rationality of certain period ratios of modular forms and even p-integrality of these ratios under the assumption that p does not divide a certain L-value. The rationality is applied to give a direct construction of isogenies between new quotients of Jacobians of Shimura curves, completely independent of Faltings isogeny theorem.
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تاریخ انتشار 2006