Faculty Publications

Quasimodular Forms And Automorphic Pseudodifferential Operators Of Mixed Weight

Document Type

Article

Keywords

Automorphic pseudodifferential operators, Jacobi-like forms, Modular forms, Quasimodular forms

Journal/Book/Conference Title

Ramanujan Journal

Volume

46

Issue

1

First Page

229

Last Page

243

Abstract

Jacobi-like forms for a discrete subgroup Γ of SL(2 , R) are formal power series which generalize Jacobi forms, and they are in one-to-one correspondence with automorphic pseudodifferential operators for Γ. The well-known Cohen–Kuznetsov lifting of a modular form f provides a Jacobi-like form and therefore an automorphic pseudodifferential operator associated to f. Given a pair (λ, μ) of integers, automorphic pseudodifferential operators can be extended to those of mixed weight. We show that each coefficient of an automorphic pseudodifferential operator of mixed weight is a quasimodular form and prove the existence of a lifting of Cohen–Kuznetsov type for each quasimodular form.

Department

Department of Mathematics

Original Publication Date

5-1-2018

DOI of published version

10.1007/s11139-017-9931-4

Repository

UNI ScholarWorks, Rod Library, University of Northern Iowa

Language

en

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