On Kleinian mock modular forms

TL;DR

This paper introduces a new explicit method for constructing harmonic weak Maass forms related to weight 2 newforms, utilizing a novel non-analytic completion of the Kleinian zeta-function from Abelian functions theory.

Contribution

It provides a computationally efficient construction of harmonic weak Maass forms using a new non-analytic completion of the Kleinian zeta-function.

Findings

Explicit construction of harmonic weak Maass forms mapping to weight 2 newforms

Introduction of a new non-analytic Kleinian zeta-function completion

Enhanced computational methods for Maass forms

Abstract

We give an explicit and computationally efficient construction of harmonic weak Maass forms which map to weight $2$ newforms under the $\xi$-operator. Our work uses a new non-analytic completion of the Kleinian $\zeta$-function from the theory of Abelian functions.