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Nonvanishing of Central Values of $L$-functions of Newforms in $S_2 (\Gamma_0 (dp^2))$ Twisted by Quadratic Characters

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorLE FOURN, Samuel
dc.date.accessioned2024-04-04T03:07:26Z
dc.date.available2024-04-04T03:07:26Z
dc.date.issued2017
dc.identifier.issn0008-4395
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193441
dc.description.abstractEnWe prove that for d ∈ {2, 3, 5, 7, 13} and K a quadratic (or rational) eld of discriminant D and Dirichlet character χ, if a prime p is large enough compared to D, there is a newform f ∈ S2(Γ0(dp 2)) with sign (+1) with respect to the Atkin-Lehner involution w p 2 such that L(f ⊗ χ, 1) = 0. This result is obtained through an estimate of a weighted sum of twists of L-functions which generalises a result of Ellenberg. It relies on the approximate functional equation for the L-functions L(f ⊗ χ, ·) and a Petersson trace formula restricted to Atkin-Lehner eigenspaces. An application of this nonvanishing theorem will be given in terms of existence of rank zero quotients of some twisted jacobians, which generalises a result of Darmon and Merel. Keywords. Nonvanishing of L-functions of modular forms, Petersson trace formula, rank zero quotients of jacobians. MSC201 11F67 and 14J15.
dc.language.isoen
dc.publisherCambridge University Press
dc.title.enNonvanishing of Central Values of $L$-functions of Newforms in $S_2 (\Gamma_0 (dp^2))$ Twisted by Quadratic Characters
dc.typeArticle de revue
dc.identifier.doi10.4153/CMB-2016-085-6
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
bordeaux.journalCanadian Mathematical Bulletin
bordeaux.page329 - 349
bordeaux.volume60
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue2
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01668070
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01668070v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Canadian%20Mathematical%20Bulletin&rft.date=2017&rft.volume=60&rft.issue=2&rft.spage=329%20-%20349&rft.epage=329%20-%20349&rft.eissn=0008-4395&rft.issn=0008-4395&rft.au=LE%20FOURN,%20Samuel&rft.genre=article


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