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- W1984205232 abstract "We prove that the theta correspondence for the dual pair $({widetilde{textup{SL}_2}}, textit{PB}^times)$ , for B an indefinite quaternion algebra over ℚ, acting on modular forms of odd square-free level, 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." @default.
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- W1984205232 date "2008-12-19" @default.
- W1984205232 modified "2023-09-27" @default.
- W1984205232 title "Arithmetic properties of the Shimura–Shintani–Waldspurger correspondence" @default.
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- W1984205232 doi "https://doi.org/10.1007/s00222-008-0169-z" @default.
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