Functional Equation for p-adic Rankin-Selberg L-functions

Abstract

We prove a functional equation for the three-variable $p$-adic $L$-function attached to the Rankin-Selberg convolution of a Coleman family and a CM Hida family, which was studied by Loeffler and Zerbes. Consequentially, we deduce that an anticyclotomic $p$-adic $L$-function attached to a $p$-non-ordinary modular form vanishes identically in the indefinite setting.

Minor update. We have corrected some misprints and expanded some of the proofs

References in corpus (3)

• Rankin--Eisenstein classes in Coleman families
• On the asymptotic growth of Bloch-Kato-Shafarevich-Tate groups of modular forms over cyclotomic extensions
• A note on p-adic Rankin--Selberg L-functions