L-Series of Harmonic Maass Forms and a Summation Formula for Harmonic Lifts

Abstract

We introduce an -series associated with harmonic Maass forms and prove their functional equations. We establish converse theorems for these -series and, as an application, we formulate and prove a summation formula for the holomorphic part of a harmonic lift of a given cusp form. © 2022 The Author(s). Published by Oxford University Press.