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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Zagier duality for harmonic weak Maass forms of integral weight


Authors: Bumkyu Cho and YoungJu Choie
Journal: Proc. Amer. Math. Soc. 139 (2011), 787-797
MSC (2010): Primary 11F11, 11F30; Secondary 11F37, 11F50
Published electronically: October 27, 2010
MathSciNet review: 2745632
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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, Hyoja-dong, Nam-gu, Pohang-si, Gyeongsangbuk-do 790-784, 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/S0002-9939-2010-10751-7
PII: S 0002-9939(2010)10751-7
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 Tae-Joon Park POSTECH Postdoctoral Fellowship, and NRF 2010-0008426
The second author was partially supported by NRF20090083919 and NRF2009-0094069
Communicated by: Ken Ono
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.