Series expansion of the period function and representations of Hecke operators

Dohoon Choi, Subong Lim, Tobias Mühlenbruch, Wissam Raji

Research output: Contribution to journalArticle


The period polynomial of a cusp form of an integral weight plays an important role in the number theory. In this paper, we study the period function of a cusp form of real weight. We obtain a series expansion of the period function of a cusp form of real weight for SL(2,Z) by using the binomial expansion. Furthermore, we study two kinds of Hecke operators acting on cusp forms and period functions, respectively. With these Hecke operators we show that there is a Hecke-equivariant isomorphism between the space of cusp forms and the space of period functions. As an application, we obtain a formula for a certain L-value of a Hecke eigenform by using the series expansion of its period function.

Original languageEnglish
Pages (from-to)301-340
Number of pages40
JournalJournal of Number Theory
Publication statusPublished - 2017 Feb 1
Externally publishedYes



  • Eichler–Shimura cohomology
  • Hecke operators
  • Period functions

ASJC Scopus subject areas

  • Algebra and Number Theory

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