Heegner cycles and congruences between anticyclotomic p-adic L-functions over CM-extensions

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dc.contributor.authorDelbourgo, Danielen_NZ
dc.contributor.authorLei, Antonioen_NZ
dc.date.accessioned2020-09-29T20:24:43Z
dc.date.available2020-09-29T20:24:43Z
dc.date.issued2020en_NZ
dc.description.abstractLet E be a CM-field, and suppose that f, g are two primitive Hilbert cusp forms over E⁺ of weight 2 satisfying a congruence modulo λʳ. Under appropriate hypotheses, we show that the complex L-values of f and g twisted by a ring class character over E, and divided by the motivic periods, also satisfy a congruence relation mod λʳ (after removing some Euler factors). We treat both the even and odd cases for the sign in the functional equation – this generalizes classical work of Vatsal [23] on congruences between elliptic modular forms twisted by Dirichlet characters. In the odd case, we also show that the p-adic logarithms of Heegner points attached to f and g satisfy a congruence relation modulo λʳ, thus extending recent work of Kriz and Li [17] concerning elliptic modular forms.
dc.format.mimetypeapplication/pdf
dc.identifier.citationDelbourgo, D., & Lei, A. (2020). Heegner cycles and congruences between anticyclotomic p-adic L-functions over CM-extensions. New York Journal of Mathematics, 26, 496–525.en
dc.identifier.issn1076-9803en_NZ
dc.identifier.urihttps://hdl.handle.net/10289/13861
dc.language.isoenen_NZ
dc.publisherElectronic Journals Projecten_NZ
dc.relation.isPartOfNew York Journal of Mathematicsen_NZ
dc.relation.urihttp://nyjm.albany.edu/j/2020/26-24v.pdf
dc.rights© 2020 copyright with the authors.
dc.subjectScience & Technologyen_NZ
dc.subjectPhysical Sciencesen_NZ
dc.subjectMathematicsen_NZ
dc.subjectIwasawa theoryen_NZ
dc.subjectp-adic L-functionsen_NZ
dc.subjectHilbert modular formsen_NZ
dc.subjectGROSS-ZAGIERen_NZ
dc.subjectPOINTSen_NZ
dc.subjectHEIGHTSen_NZ
dc.subjectFORMULAen_NZ
dc.subjectCURVESen_NZ
dc.subjectVALUESen_NZ
dc.titleHeegner cycles and congruences between anticyclotomic p-adic L-functions over CM-extensionsen_NZ
dc.typeJournal Article
pubs.begin-page496
pubs.elements-id251536
pubs.end-page525
pubs.organisational-group/Waikato
pubs.organisational-group/Waikato/2024 PBRF
pubs.organisational-group/Waikato/DHECS
pubs.organisational-group/Waikato/DHECS/2024 PBRF - DHEC
pubs.organisational-group/Waikato/DHECS/SCMS
pubs.organisational-group/Waikato/DHECS/SCMS/2024 PBRF - SCMS
pubs.publication-statusPublisheden_NZ
pubs.user.infoDelbourgo, Daniel (delbourg@waikato.ac.nz)
pubs.volume26en_NZ
uow.verification.statusverified
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