Exceptional zeros and L-invariants of Bianchi modular forms
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Cita com:
hdl:2117/112297
Tipus de documentArticle
Data publicació2018
Condicions d'accésAccés obert
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Reconeixement-NoComercial-SenseObraDerivada 3.0 Espanya
Abstract
Let f be a Bianchi modular form, that is, an automorphic form for GL2 over an imaginary quadratic field F. In this paper, we prove an exceptional zero conjecture in the case where f is new at a prime above p. More precisely, for each prime p of F above p we prove the existence of an Linvariant Lp, depending only on p and f, such that when the p-adic L-function of f has an exceptional zero at p, its derivative can be related to the classical L-value multiplied by Lp. The proof uses cohomological methods of Darmon and Orton, who proved similar results for GL2/Q. When p is not split and f is the base-change of a classical modular form f ˜, we relate Lp to the L-invariant of f ˜, resolving a conjecture of Trifkovi´c in this case.
CitacióBarrera, D., Williams, C. Exceptional zeros and L-invariants of Bianchi modular forms. "Transactions of the American Mathematical Society", 2018, p. 1-36.
ISSN0002-9947
Versió de l'editorhttps://www.ams.org/journals/tran/2019-372-01/S0002-9947-2019-07436-6/
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