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

      Delbourgo, Daniel; Lei, Antonio
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      HeegnerCMcongruences - Revised.pdf
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       nyjm.albany.edu
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      Delbourgo, 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.
      Permanent Research Commons link: https://hdl.handle.net/10289/13861
      Abstract
      Let 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.
      Date
      2020
      Type
      Journal Article
      Publisher
      Electronic Journals Project
      Rights
      © 2020 copyright with the authors.
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      • Computing and Mathematical Sciences Papers [1455]
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