p-adic L-functions via local-global interpolation: The case of GL2× GU(1)

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Abstract

Let F be a totally real field and let E/F be a CM quadratic extension. We construct a p-adic L-function attached to Hida families for the group GL2/F× ResE/FGL1. It is characterised by an exact interpolation property for critical Rankin-Selberg L-values, at classical points corresponding to representations π X with the weights of X smaller than the weights of π. Our p-adic L-function agrees with previous results of Hida when E F splits above p or F = Q, and it is new otherwise. Exploring a method that should bear further fruits, we build it as a ratio of families of global and localWaldspurger zeta integrals, the latter constructed using the local Langlands correspondence in families. In an appendix of possibly independent recreational interest, we give a reality-TV-inspired proof of an identity concerning double factorials.

Original languageEnglish
JournalCanadian Journal of Mathematics
DOIs
StateAccepted/In press - 1 Jan 2022

ASJC Scopus subject areas

  • Mathematics (all)

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