Teitelbaum formulated a conjecture relating first derivatives of the Mazur-Swinnerton-Dyer $p$-adic $L$-functions attached to modular forms of even weight $k\ge 2$ to certain $\cal L$-invariants arising from Shimura curve parametrizations. This article formulates an analogue of Teitelbaum's conjecture in which the cyclotomic $\Bbb {Z}$_p$ extension of $\Bbb Q$ is replaced by the anticyclotomic $\Bbb{Z}$_p$-extension of an imaginary quadratic field. This analogue is then proved by using the Cerednik-Drinfeld theory of $p$-adic uniformisation of Shimura curves.

Teitelbaum's expectional zero conjecture in the anticyclotomic setting / M. Bertolini, H. Darmon, A. Iovita, M. Spiess. - In: AMERICAN JOURNAL OF MATHEMATICS. - ISSN 0002-9327. - 124:2(2002), pp. 411-449.

Teitelbaum's expectional zero conjecture in the anticyclotomic setting

M. Bertolini;
2002

Abstract

Teitelbaum formulated a conjecture relating first derivatives of the Mazur-Swinnerton-Dyer $p$-adic $L$-functions attached to modular forms of even weight $k\ge 2$ to certain $\cal L$-invariants arising from Shimura curve parametrizations. This article formulates an analogue of Teitelbaum's conjecture in which the cyclotomic $\Bbb {Z}$_p$ extension of $\Bbb Q$ is replaced by the anticyclotomic $\Bbb{Z}$_p$-extension of an imaginary quadratic field. This analogue is then proved by using the Cerednik-Drinfeld theory of $p$-adic uniformisation of Shimura curves.
2002
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/25633
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