Abstract
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.
Original language | English |
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Pages (from-to) | 429-441 |
Number of pages | 13 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 411 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2014 Mar 1 |
Externally published | Yes |
Keywords
- Eichler integral
- Harmonic weak Maass form
- Period function
- Period polynomial
ASJC Scopus subject areas
- Analysis
- Applied Mathematics