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arXiv · 2501.03673

A generalized Rubin formula for Hecke characters

Matteo Longo·Stefano Vigni·Shilun Wang
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Abstract

The goal of this paper is to generalize Rubin's theorem on values of Katz's $p$-adic $L$-function outside the range of interpolation from the case of Hecke characters of CM elliptic curves to more general self-dual algebraic Hecke characters. We follow the approach by Bertolini-Darmon-Prasanna, based on generalized Heegner cycles, which we extend from characters of imaginary quadratic fields of infinity type $(1,0)$ to characters of infinity type $(1+\ell,-\ell)$ for an integer $\ell\geq0$.

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Matteo Longo, Stefano Vigni, Shilun Wang. 2025-01-07. A generalized Rubin formula for Hecke characters. https://arxiv.org/abs/2501.03673

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