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

DOI:
https://doi.org/10.1090/S0002-9939-2010-10751-7

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:
https://doi.org/10.1090/S0002-9939-2010-10751-7

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.