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dc.contributor.authorBarrera Salazar, Daniel Roberto
dc.contributor.authorWilliams, Chris
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2017-12-19T18:21:03Z
dc.date.available2017-12-19T18:21:03Z
dc.date.issued2018
dc.identifier.citationBarrera, D., Williams, C. Exceptional zeros and L-invariants of Bianchi modular forms. "Transactions of the American Mathematical Society", 2018, p. 1-36.
dc.identifier.issn0002-9947
dc.identifier.urihttp://hdl.handle.net/2117/112297
dc.description.abstractLet 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.
dc.format.extent36 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
dc.subject.lcshAlgebra
dc.subject.lcshMathematics
dc.subject.lcshArithmetic functions
dc.titleExceptional zeros and L-invariants of Bianchi modular forms
dc.typeArticle
dc.subject.lemacAritmètica
dc.subject.lemacFuncions algèbriques
dc.identifier.doi10.1090/tran/7436
dc.relation.publisherversionhttps://www.ams.org/journals/tran/2019-372-01/S0002-9947-2019-07436-6/
dc.rights.accessOpen Access
local.identifier.drac21681720
dc.description.versionPostprint (author's final draft)
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020/682152/EU/Euler systems and the conjectures of Birch and Swinnerton-Dyer, Bloch and Kato/BSD
local.citation.authorBarrera, D.; Williams, C.
local.citation.publicationNameTransactions of the American Mathematical Society
local.citation.volume372
local.citation.number1
local.citation.startingPage1
local.citation.endingPage36


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Attribution-NonCommercial-NoDerivs 3.0 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain