Maass wave forms, quantum modular forms and Hecke operators

TL;DR

This paper demonstrates that specific Maass wave forms are Hecke eigenforms and derives new identities for their coefficients involving roots of unity, advancing understanding in automorphic forms and number theory.

Contribution

It establishes that Cohen's and Li-Ngo-Rhoades' Maass wave forms are Hecke eigenforms and derives new identities for their Fourier coefficients.

Findings

Proves these Maass wave forms are Hecke eigenforms.

Derives identities for Fourier coefficients involving roots of unity.

Enhances understanding of automorphic forms and Hecke operators.

Abstract

We prove that Cohen's Maass wave form and Li-Ngo-Rhoades' Maass wave form are Hecke eigenforms with respect to certain Hecke operators. As a corollary, we find new identities of the $p$th coefficients of these Maass wave forms in terms of $p$th root of unities.