Critical p-adic L-function

TL;DR

This paper constructs p-adic L-functions for critical modular forms and demonstrates their extension to a two-variable p-adic L-function over the eigencurve, advancing understanding of p-adic properties of modular forms.

Contribution

It introduces a novel two-variable p-adic L-function associated with critical modular forms, extending local constructions globally on the eigencurve.

Findings

Construction of p-adic L-functions for critical modular forms

Extension to a two-variable p-adic L-function on the eigencurve

Local-to-global compatibility of the p-adic L-functions

Abstract

We attach p-adic L-functions to critical modular forms and study them. We prove that those L-functions fit in a two-variables p-adic L-function defined locally everywhere on the eigencurve.