Two variable anticyclotomic p-adic L-functions for Hida families

TL;DR

This paper introduces a second p-adic variable in the anticyclotomic p-adic Rankin--Selberg L-function by considering Hida families, expanding the framework for studying p-adic L-functions associated with modular forms and imaginary quadratic fields.

Contribution

It extends the theory of anticyclotomic p-adic L-functions by incorporating a second variable through Hida families, providing a new perspective for p-adic L-function analysis.

Findings

Defined a new two-variable p-adic L-function for Hida families.

Established foundational properties of the new L-function.

Enhanced understanding of p-adic variation in automorphic forms.

Abstract

For the anticyclotomic p-adic Rankin--Selberg L-function attached to a fixed Hecke eigenform and an imaginary quadratic field we introduce the second p-adic variable by considering Hida families of Hecke eigenforms parametrized by the weight.