Eichler integrals and harmonic weak Maass forms

Dohoon Choi, Byungchan Kim, Subong Lim

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 languageEnglish
Pages (from-to)429-441
Number of pages13
JournalJournal of Mathematical Analysis and Applications
Volume411
Issue number1
DOIs
Publication statusPublished - 2014 Mar 1

    Fingerprint

Keywords

  • Eichler integral
  • Harmonic weak Maass form
  • Period function
  • Period polynomial

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this