P-adic Rankin-Selberg L-functions in universal deformation families and functional equations

2024/05/21 by Zeping Hao, David Loeffler, Hao, Zeping +1 · 1 citation
Mathematics · #11F67 #11F80 #11R23 #Advanced Algebra and Geometry #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2405.12611

openalex publication_date 2024/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

We construct a p-adic Rankin-Selberg L-function associated to the product of two families of modular forms, where the first is an ordinary (Hida) family, and the second an arbitrary universal-deformation family (without any ordinarity condition at p). This gives a function on a 4-dimensional base space - strictly larger than the ordinary eigenvariety, which is 3-dimensional in this case. We prove our p-adic L-function interpolates all critical values of the Rankin-Selberg L-functions for the classical specialisations of our family, and derive a functional equation for our p-adic L-function.

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