Quasimodular forms and automorphic pseudodifferential operators of mixed weight
Automorphic pseudodifferential operators, Jacobi-like forms, Modular forms, Quasimodular forms
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.
Original Publication Date
DOI of published version
UNI ScholarWorks, Rod Library, University of Northern Iowa
Lee, Min Ho, "Quasimodular forms and automorphic pseudodifferential operators of mixed weight" (2018). Faculty Publications. 718.