# Harmonic Maass form eigencurves

## TL;DR

This paper constructs families of harmonic Maass Hecke eigenforms, providing an eigencurve analogue in this context, and develops p-adic harmonic Maass forms, advancing the understanding of their structure and properties.

## Contribution

It introduces the first known eigencurve-type objects for harmonic Maass forms and constructs p-adic harmonic Maass forms, answering longstanding questions.

## Key findings

- Constructed two families of harmonic Maass Hecke eigenforms.
- Established the existence of an eigencurve-type object for harmonic Maass forms.
- Developed p-adic harmonic Maass forms in the sense of Serre.

## Abstract

We construct two families of harmonic Maass Hecke eigenforms. This construction answers a question of Mazur about the existence of an "eigencurve-type" object in the world of harmonic Maass forms. Using these families, we construct $p$-adic harmonic Maass forms in the sense of Serre.