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      Exceptional zeros of p-adic L-functions over non-abelian extensions

      Delbourgo, Daniel
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      Accepted-paper.pdf
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      DOI
       10.1017/S0017089515000245
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      Delbourgo, D. (2014). Exceptional zeros of p-adic L-functions over non-abelian extensions. Glasgow Mathematical Journal, First View. http://doi.org/10.1017/S0017089515000245
      Permanent Research Commons link: https://hdl.handle.net/10289/9749
      Abstract
      Suppose E is an elliptic curve over , and p > 3 is a split multiplicative prime for E. Let q = p be an auxiliary prime, and fix an integer m coprime to pq. We prove the generalised Mazur–Tate–Teitelbaum conjecture for E at the prime p, over number fields K ⊂ μq∞ , q∞√m such that p remains inert in K ∩ (μq∞ ) +. The proof makes use of an improved p-adic L-function, which can be associated to the Rankin convolution of two Hilbert modular forms of unequal parallel weight.
      Date
      2014
      Type
      Journal Article
      Publisher
      Cambridge University Press (CUP)
      Collections
      • Computing and Mathematical Sciences Papers [1455]
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