The exceptional zero conjecture for Hilbert modular forms
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AbstractUsing ap-adic analogue of the convolution method of Rankin–Selberg and Shimura, we construct the two-variablep-adicL-function of a Hida family of Hilbert modular eigenforms of parallel weight. It is shown that the conditions of Greenberg–Stevens [R. Greenberg and G. Stevens,p-adic L-functions and p-adic periods of modular forms, Invent. Math.111(1993), 407–447] are satisfied, from which we deduce special cases of the Mazur–Tate–Teitelbaum conjecture in the Hilbert modular setting.
1987 ◽
Vol 55
(4)
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pp. 765-838
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2013 ◽
Vol 49
(2)
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pp. 221-227
2008 ◽
Vol 128
(11)
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pp. 2874-2889
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