## Illinois Journal of Mathematics

### Eichler integrals for Maass cusp forms of half-integral weight

#### Abstract

In this paper, we define and discuss Eichler integrals for Maass cusp forms of half-integral weight on the full modular group. We discuss nearly periodic functions associated to the Eichler integrals, introduce period functions for such Maass cusp forms, and show that the nearly periodic functions and the period functions are closely related. Those functions are extensions of the periodic functions and period functions for Maass cusp forms of weight $0$ on the full modular group introduced by Lewis and Zagier.

#### Article information

Source
Illinois J. Math., Volume 57, Number 2 (2013), 445-475.

Dates
First available in Project Euclid: 19 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1408453590

Mathematical Reviews number (MathSciNet)
MR3263041

Zentralblatt MATH identifier
1312.11034

#### Citation

Mühlenbruch, T.; Raji, W. Eichler integrals for Maass cusp forms of half-integral weight. Illinois J. Math. 57 (2013), no. 2, 445--475. https://projecteuclid.org/euclid.ijm/1408453590

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