Bringmann, Kathrin, Ehlen, Stephan and Schwagenscheidt, Markus ORCID: 0000-0002-8214-3106
(2021).
On the Modular Completion of Certain Generating Functions.
Int. Math. Res. Notices, 2021 (8).
S. 6331 - 6373.
OXFORD:
OXFORD UNIV PRESS.
ISSN 1687-0247
Abstract
We complete several generating functions to non-holomorphic modular forms in two variables. For instance, we consider the generating function of a natural family of meromorphic modular forms of weight two. We then show that this generating series can be completed to a smooth, non-holomorphic modular form of weights 3/2 and two. Moreover, it turns out that the same function is also a modular completion of the generating function of weakly holomorphic modular forms of weight 3/2, which prominently appear in work of Zagier [27] on traces of singular moduli.
Item Type: | Journal Article | ||||||||||||||||
Creators: |
|
||||||||||||||||
URN: | urn:nbn:de:hbz:38-566290 | ||||||||||||||||
DOI: | 10.1093/imrn/rnz338 | ||||||||||||||||
Journal or Publication Title: | Int. Math. Res. Notices | ||||||||||||||||
Volume: | 2021 | ||||||||||||||||
Number: | 8 | ||||||||||||||||
Page Range: | S. 6331 - 6373 | ||||||||||||||||
Date: | 2021 | ||||||||||||||||
Publisher: | OXFORD UNIV PRESS | ||||||||||||||||
Place of Publication: | OXFORD | ||||||||||||||||
ISSN: | 1687-0247 | ||||||||||||||||
Language: | English | ||||||||||||||||
Faculty: | Unspecified | ||||||||||||||||
Divisions: | Unspecified | ||||||||||||||||
Subjects: | no entry | ||||||||||||||||
Uncontrolled Keywords: |
|
||||||||||||||||
URI: | http://kups.ub.uni-koeln.de/id/eprint/56629 |
Downloads
Downloads per month over past year
Altmetric
Export
Actions (login required)
![]() |
View Item |