Zagier duality for harmonic weak Maass forms of integral weight
Authors:
Bumkyu Cho and YoungJu Choie
Journal:
Proc. Amer. Math. Soc. 139 (2011), 787797
MSC (2010):
Primary 11F11, 11F30; Secondary 11F37, 11F50
Published electronically:
October 27, 2010
MathSciNet review:
2745632
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Additional Information
Abstract: We show the existence of ``Zagier duality'' between vector valued harmonic weak Maass forms and vector valued weakly holomorphic modular forms of integral weight. This duality phenomenon arises naturally in the context of harmonic weak Maass forms as developed in recent works by Bruinier, Funke, Ono, and Rhoades. Concerning the isomorphism between the spaces of scalar and vector valued harmonic weak Maass forms of integral weight, Zagier duality between scalar valued ones is derived.
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Additional Information
Bumkyu Cho
Affiliation:
Department of Mathematics, Pohang University of Science and Technology, San 31, Hyojadong, Namgu, Pohangsi, Gyeongsangbukdo 790784, Republic of Korea
Email:
bam@math.kaist.ac.kr
YoungJu Choie
Affiliation:
Department of Mathematics, Pohang Mathematics Institute, POSTECH, Pohang, Republic of Korea
Email:
yjc@postech.ac.kr
DOI:
http://dx.doi.org/10.1090/S000299392010107517
Received by editor(s):
March 14, 2010
Published electronically:
October 27, 2010
Additional Notes:
The first author was partially supported by BK21 at POSTECH, the TaeJoon Park POSTECH Postdoctoral Fellowship, and NRF 20100008426
The second author was partially supported by NRF20090083919 and NRF20090094069
Communicated by:
Ken Ono
Article copyright:
© Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
