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
Recommended Citation
Lee, Min Ho, "Quasimodular Forms And Automorphic Pseudodifferential Operators Of Mixed Weight" (2018). Faculty Publications. 718.
https://scholarworks.uni.edu/facpub/718
