Derivatives of Rankin-Selberg L-functions and heights of generalized Heegner cycles

2024/08/08 by Lilienfeldt, David T. -B. G., Shnidman, Ari · 1 citation
#11G15 #11G40 #14C25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2408.04375

Abstract

Let f be a newform of weight 2k and let χ be an unramified imaginary quadratic Hecke character of infinity type (2t, 0), for some integer 0 < t ≤ k-1. We show that the central derivative of the Rankin-Selberg L-function L(f,χ,s) is, up to an explicit positive constant, equal to the Beilinson-Bloch height of a generalized Heegner cycle. This generalizes the Gross-Zagier formula (the case k = 1) and Zhang's higher weight formula (the case t=0).

Cited by

• On the Tamagawa number conjecture for modular forms twisted by anticyclotomic Hecke characters

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