Show simple item record  

dc.contributor.authorDelbourgo, Danielen_NZ
dc.contributor.authorLei, Antonioen_NZ
dc.date.accessioned2018-11-08T23:27:25Z
dc.date.available2018-11-01en_NZ
dc.date.available2018-11-08T23:27:25Z
dc.date.issued2018en_NZ
dc.identifier.citationDelbourgo, D., & Lei, A. (2018). Congruences modulo ρ between ρ-wisted Hasse-Weil L-values. Transactions of The American Mathematical Society, 370(11), 8047–8080. https://doi.org/10.1090/tran/7240en
dc.identifier.issn0002-9947en_NZ
dc.identifier.urihttps://hdl.handle.net/10289/12155
dc.description.abstractSuppose E₁ and E₂ are semistable elliptic curves over Q with good reduction at p, whose associated weight two newforms f₁ and f₂ have congruent Fourier coefficients modulo p. Let RS(E*, ρ) denote the algebraic padic L-value attached to each elliptic curve E, twisted by an irreducible Artin representation, ρ, factoring through the Kummer extension Q(μp∞, Δ1/p∞). If E₁ and E₂ have good ordinary reduction at p, we prove that RS(E₁, ρ) ≡ RS(E₂, ρ) mod p, under an integrality hypothesis for the modular symbols defined over the field cut out by Ker(ρ). Under this hypothesis, we establish that E₁ and E₂ have the same analytic λ-invariant at ρ. Alternatively, if E₁ and E₂ have good supersingular reduction at p, we show that |RS(E₁, ρ) − RS(E₂, ρ)|ₚ < p ᵒʳᵈᵖ⁽ᶜᵒⁿᵈ⁽ρ⁾⁾/². These congruences generalise some earlier work of Vatsal [Duke Math. J. 98 (1999), pp. 399–419], Shekhar–Sujatha [Trans. Amer. Math. Soc. 367 (2015), pp. 3579–3598], and Choi-Kim [Ramanujan J. 43 (2017), p. 163–195], to the false Tate curve setting.
dc.format.mimetypeapplication/pdf
dc.language.isoenen_NZ
dc.publisherAmerican Mathematical Societyen_NZ
dc.rightsThis is an author’s accepted version of an article published in the journal: Transactions of The American Mathematical Society. © 2018 Transactions of The American Mathematical Society.
dc.subjectScience & Technologyen_NZ
dc.subjectPhysical Sciencesen_NZ
dc.subjectMathematicsen_NZ
dc.subjectADIC L-FUNCTIONSen_NZ
dc.subjectELLIPTIC-CURVESen_NZ
dc.subjectIWASAWA INVARIANTSen_NZ
dc.subjectFORMSen_NZ
dc.subjectFORMULASen_NZ
dc.subjectPERIODSen_NZ
dc.titleCongruences modulo ρ between ρ-wisted Hasse-Weil L-valuesen_NZ
dc.typeJournal Article
dc.identifier.doi10.1090/tran/7240en_NZ
dc.relation.isPartOfTransactions of The American Mathematical Societyen_NZ
pubs.begin-page8047
pubs.elements-id192990
pubs.end-page8080
pubs.issue11en_NZ
pubs.publication-statusPublisheden_NZ
pubs.volume370en_NZ
dc.identifier.eissn1088-6850en_NZ


Files in this item

This item appears in the following Collection(s)

Show simple item record