A characterization of planar mixed automorphic forms

TL;DR

This paper characterizes a specific class of planar mixed automorphic forms of type (ν,μ) by relating them to traditional automorphic forms through a specialized transform, enhancing understanding of their structure.

Contribution

It introduces a new characterization of planar mixed automorphic forms of type (ν,μ) using an appropriate transform linked to Landau automorphic forms.

Findings

Provides a new representation of mixed automorphic forms

Establishes a connection with Landau automorphic forms

Enhances understanding of automorphic form structures

Abstract

We characterize the space of the so-called planar mixed automorphic forms of type $(\nu,\mu)$ with respect to an equivariant pair $(\rho,\tau)$ as the image, by an appropriate transform, of the usual (Landau) automorphic forms involving special multiplier.