TY - JOUR
T1 - Eichler integrals and harmonic weak Maass forms
AU - Choi, Dohoon
AU - Kim, Byungchan
AU - Lim, Subong
N1 - Funding Information:
Dohoon Choi was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( NRF2010-0022180 ). Byungchan Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( NRF2011-0009199 ).
PY - 2014/3/1
Y1 - 2014/3/1
N2 - Recently, K. Bringmann, P. Guerzhoy, Z. Kent and K. Ono studied the connection between Eichler integrals and the holomorphic parts of harmonic weak Maass forms on the full modular group. In this article, we extend their result to more general groups, namely, H-groups by employing the theory of supplementary functions introduced and developed by M.I. Knopp and S.Y. Husseini. In particular, we show that the set of Eichler integrals, which have polynomial period functions, is the same as the set of holomorphic parts of harmonic weak Maass forms of which the non-holomorphic parts are certain period integrals of cusp forms. From this we deduce relations among period functions for harmonic weak Maass forms.
AB - Recently, K. Bringmann, P. Guerzhoy, Z. Kent and K. Ono studied the connection between Eichler integrals and the holomorphic parts of harmonic weak Maass forms on the full modular group. In this article, we extend their result to more general groups, namely, H-groups by employing the theory of supplementary functions introduced and developed by M.I. Knopp and S.Y. Husseini. In particular, we show that the set of Eichler integrals, which have polynomial period functions, is the same as the set of holomorphic parts of harmonic weak Maass forms of which the non-holomorphic parts are certain period integrals of cusp forms. From this we deduce relations among period functions for harmonic weak Maass forms.
KW - Eichler integral
KW - Harmonic weak Maass form
KW - Period function
KW - Period polynomial
UR - http://www.scopus.com/inward/record.url?scp=84886298805&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2013.09.052
DO - 10.1016/j.jmaa.2013.09.052
M3 - Article
AN - SCOPUS:84886298805
VL - 411
SP - 429
EP - 441
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 1
ER -