Four-variable p-adic triple product L-functions and the trivial zero conjecture
Journal
Mathematische Annalen
Date Issued
2023-01-01
Author(s)
Yamana, Shunsuke
Abstract
We construct the four-variable primitive p-adic L-functions associated with the triple product of Hida families and prove the explicit interpolation formulae at all critical points in the balanced range. Our construction is to carry out the p-adic interpolation of Garrett’s integral representation of triple product L-functions via the p-adic Rankin-Selberg convolution method. The main novelty in this paper is the construction and the patching of four p-adic families of the pull-back of nearly holomorphic Siegel Eisenstein series on GSp (6) . As an application, we obtain the cyclotomic p-adic L-function for the motive associated with the triple product of p-ordinary elliptic curves and prove the trivial zero conjecture for this motive. In particular, this proves the first cases of the Greenberg-Benois trivial zero conjecture where multiple trivial zeros are present and the Galois representation is not of GL (2) -type.
Type
journal article