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Structure of the space of polyharmonic Maass forms with an application to L-values
Title
Structure of the space of polyharmonic Maass forms with an application to L-values
Authors
Hwang
;
Jihyun
;
Lee
;
Yoonjin
Ewha Authors
이윤진
SCOPUS Author ID
이윤진
Issue Date
2024
Journal Title
Journal of Mathematical Analysis and Applications
ISSN
0022-247X
Citation
Journal of Mathematical Analysis and Applications vol. 538, no. 2
Keywords
L-series
;
Polyharmonic Maass forms
;
Weakly holomorphic modular forms
Indexed
SCIE; SCOPUS
Document Type
Article
Abstract
A polyharmonic Maass form introduced by Lagarias and Rhoades is a generalization of a harmonic Maass form in a sense. In this paper, we construct some bases for the spaces of polyharmonic Maass forms from the structure of the spaces of weakly holomorphic modular forms for prime levels or square-free levels. Furthermore, we relate the polyharmonic Maass forms of depth 1 or depth 3/2 to the L-series of holomorphic cusp forms for square-free levels. © 2024 Elsevier Inc.
DOI
10.1016/j.jmaa.2024.128452
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