Rankin-Selberg L-functions in cyclotomic towers, I

2012/07/06 by Jeanine Van Order, Van Order, Jeanine
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1207.1672

openalex publication_date 2012/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We formulate and for the most part prove a conjecture in the style of Mazur-Greenberg for the nonvanishing of central values of Rankin-Selberg L-functions attached to elliptic curves in abelian extensions of imaginary quadratic fields. This in particular generalizes the theorem of Rohrlich on L-functions of elliptic curves in cyclotomic towers to the setting of abelian extensions of imaginary quadratic fields, corresponding to families of degree-four L-functions given by GL(2)\timesGL(2) Rankin-Selberg L-functions. It also generalizes the theorems of Rohrlich, Greenberg, Vatsal, and Cornut for L-functions of elliptic curves in Z_p²-extensions of imaginary quadratic fields.

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