$\Lambda$-adic modular symbols and several variable $p$-adic L-functions over totally real fields

TL;DR

This paper constructs a two-variable $p$-adic L-function over totally real fields by interpolating cohomology classes associated with families of Hilbert modular forms, extending the theory of $p$-adic L-functions.

Contribution

It introduces a novel method to interpolate cohomology classes for Hilbert modular forms, leading to a new two-variable $p$-adic L-function over totally real fields.

Findings

Constructed a two-variable $p$-adic L-function

Interpolates one-variable $p$-adic L-functions

Advances understanding of $p$-adic properties of Hilbert modular forms

Abstract

We interpolate cohomology classes attached to families of Hilbert modular forms. Using this we construct a two variable $p$-adic L-function which interpolates one variable $p$-adic L-functions.