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Let \(E/\mathbb Q\) be an elliptic curve having multiplicative reduction at a prime p. Let (g, h) be a pair of eigenforms of weight 1 arising as the theta series of an imaginary quadratic field K, and assume that the triple-product L-function L(f, g, h, s) is self-dual and does not vanish at the central critical point \(s=1\) . The main result of this article is a formula expressing the value of the associated triple-product p-adic L-function at a point of weights (2, 1, 1) lying outside the region of classical interpolation to the Kolyvagin classes associated by Bertolini and Darmon to a system of Heegner points on E.

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A p-Adic Gross-Zagier Formula for the Triple p-Adic L-Function at Non-crystalline Points

  • 会议论文

  • 发表日期：

    2026年

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  • Francesca Gatti,
  • Victor Rotger

摘要

Let \(E/\mathbb Q\) be an elliptic curve having multiplicative reduction at a prime p. Let (g, h) be a pair of eigenforms of weight 1 arising as the theta series of an imaginary quadratic field K, and assume that the triple-product L-function L(f, g, h, s) is self-dual and does not vanish at the central critical point \(s=1\) . The main result of this article is a formula expressing the value of the associated triple-product p-adic L-function at a point of weights (2, 1, 1) lying outside the region of classical interpolation to the Kolyvagin classes associated by Bertolini and Darmon to a system of Heegner points on E.