Polyharmonic Maass forms for PSL(2, Z)

TL;DR

This paper explores polyharmonic Maass forms of even weight on PSL(2, Z), extending classical Maass forms, and investigates their relation to Eisenstein series and differential operators.

Contribution

It introduces a framework for polyharmonic Maass forms, generalizing classical Maass forms, and clarifies the role of Eisenstein series and differential operators in this context.

Findings

Polyharmonic Maass forms generalize classical Maass forms.

Real-analytic Eisenstein series are central to the theory.

Differential operators relate different forms within the framework.

Abstract

We discuss polyharmonic Maass forms of even integer weight on PSL(2, Z)\H, which are a generalization of classical Maass forms. We explain the role of real-analytic Eisenstein series E_k(z, s) and the differential operator $\partial/\partial s$ in this theory.