p-adic Asai and twisted triple product L-functions for finite slope families

2025/04/16 by Kazi, Ananyo, Loeffler, David
#11F33 #11F41 #14G35 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2504.12066

Abstract

We define a two-variable p-adic Asai L-function for a finite-slope family of Hilbert modular forms over a real quadratic field (with one component of the weight, and the cyclotomic twist variable, varying independently); and a two-variable ``twisted triple product'' L-function, interpolating the central L-value of the tensor product of such a family with a family of elliptic modular forms. The former construction generalizes a construction due to Grossi, Zerbes and the second author for ordinary families; the latter is a counterpart of the twisted triple product L-function of arXiv:2401.13230, but differs in that it interpolates classical L-values in a different range of weights, in which the dominant weight comes from the Hilbert modular form. Our construction relies on a ``nearly-overconvergent'' version of higher Coleman theory for Hilbert modular surfaces.

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