A generalized Rubin formula for Hecke characters

2025/01/07 by Longo, Matteo, Vigni, Stefano, Wang, Shilun
#11G40 #14C15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2501.03673

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+ℓ,-ℓ) for an integer ℓ≥0.

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