Quasimodular forms and automorphic pseudodifferential operators of mixed weight View Full Text


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Article Info

DATE

2018-05

AUTHORS

Min Ho Lee

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. More... »

PAGES

229-243

References to SciGraph publications

Journal

TITLE

The Ramanujan Journal

ISSUE

1

VOLUME

46

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11139-017-9931-4

DOI

http://dx.doi.org/10.1007/s11139-017-9931-4

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1091284417


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