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Mock modular period functions and $ L$-functions of cusp forms in higher level cases


Authors: SoYoung Choi and Chang Heon Kim
Journal: Proc. Amer. Math. Soc. 142 (2014), 3369-3386
MSC (2010): Primary 11F11, 11F67; Secondary 11F37
DOI: https://doi.org/10.1090/S0002-9939-2014-12073-9
Published electronically: June 19, 2014
MathSciNet review: 3238414
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Abstract: Generalizing the results of Bringmann, Guerzhoy, Kent and Ono, we investigate mock modular period polynomials associated to harmonic Maass forms for $ \Gamma _0^+(p)$. In particular, using period relations generated from the period polynomials, we derive congruence relations involving the critical values of modular $ L$-functions and show that these congruence relations are indeed equalities by using integral representations of nonholomorphic parts of harmonic Maass forms.


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Additional Information

SoYoung Choi
Affiliation: Department of Mathematics Education, Dongguk University-Gyeongju, 123 Dongdae-ro, Gyeongju, Gyeongbuk, 780-714, Republic of Korea
Email: young@dongguk.ac.kr

Chang Heon Kim
Affiliation: Department of Mathematics and Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Republic of Korea
Address at time of publication: Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea
Email: chhkim@skku.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12073-9
Keywords: Weakly holomorphic modular forms, mock modular forms, period polynomials
Received by editor(s): September 5, 2012
Received by editor(s) in revised form: September 19, 2012, and October 20, 2012
Published electronically: June 19, 2014
Additional Notes: The first author was supported by the Dongguk University Research fund of 2013 and by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2012R1A1A3011711)
The second author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2013R1A1A2A10004632)
Communicated by: Ken Ono
Article copyright: © Copyright 2014 American Mathematical Society