On special zeros of p-adic L-functions of Hilbert modular forms

Spieß M (2014)
Inventiones mathematicae 196(1): 69-138.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
Abstract / Bemerkung
Let E be a modular elliptic curve over a totally real number field F. We prove the weak exceptional zero conjecture which links a (higher) derivative of the p-adic L-function attached to E to certain p-adic periods attached to the corresponding Hilbert modular form at the places above p where E has split multiplicative reduction. Under some mild restrictions on p and the conductor of E we deduce the exceptional zero conjecture in the strong form (i.e. where the automorphic p-adic periods are replaced by the -invariants of E defined in terms of Tate periods) from a special case proved earlier by Mok. Crucial for our method is a new construction of the p-adic L-function of E in terms of local data.
Erscheinungsjahr
Zeitschriftentitel
Inventiones mathematicae
Band
196
Ausgabe
1
Seite(n)
69-138
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PUB-ID

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Spieß M. On special zeros of p-adic L-functions of Hilbert modular forms. Inventiones mathematicae. 2014;196(1):69-138.
Spieß, M. (2014). On special zeros of p-adic L-functions of Hilbert modular forms. Inventiones mathematicae, 196(1), 69-138. doi:10.1007/s00222-013-0465-0
Spieß, M. (2014). On special zeros of p-adic L-functions of Hilbert modular forms. Inventiones mathematicae 196, 69-138.
Spieß, M., 2014. On special zeros of p-adic L-functions of Hilbert modular forms. Inventiones mathematicae, 196(1), p 69-138.
M. Spieß, “On special zeros of p-adic L-functions of Hilbert modular forms”, Inventiones mathematicae, vol. 196, 2014, pp. 69-138.
Spieß, M.: On special zeros of p-adic L-functions of Hilbert modular forms. Inventiones mathematicae. 196, 69-138 (2014).
Spieß, Michael. “On special zeros of p-adic L-functions of Hilbert modular forms”. Inventiones mathematicae 196.1 (2014): 69-138.