# q-series and weight 3/2 Maass forms

@article{Bringmann2009qseriesAW, title={q-series and weight 3/2 Maass forms}, author={Kathrin Bringmann and Amanda Folsom and Ken Ono}, journal={Compositio Mathematica}, year={2009}, volume={145}, pages={541 - 552} }

Abstract Despite the presence of many famous examples, the precise interplay between basic hypergeometric series and modular forms remains a mystery. We consider this problem for canonical spaces of weight 3/2 harmonic Maass forms. Using recent work of Zwegers, we exhibit forms that have the property that their holomorphic parts arise from Lerch-type series, which in turn may be formulated in terms of the Rogers–Fine basic hypergeometric series.

## 22 Citations

ARITHMETIC PROPERTIES OF CERTAIN LEVEL ONE MOCK MODULAR FORMS

- Mathematics
- 2010

In a recent work, Bringmann and Ono [4] show that Ramanujan's f(q) mock theta function is the holomorphic projection of a harmonic weak Maass form of weight 1/2. In this paper, we extend the work of…

Mock period functions, sesquiharmonic Maass forms, and non-critical values of L-functions

- Mathematics
- 2011

A MAASS LIFTING OF Θ 3 AND CLASS NUMBERS OF REAL AND IMAGINARY QUADRATIC FIELDS

- Mathematics
- 2011

We give an explicit construct of a harmonic weak Maass form FΘ that is a “lift” of Θ3, where Θ is the classical Jacobi theta function. Just as the Fourier coefficients of Θ3 are related to class…

$p$-adic properties of Maass forms arising from theta series

- Mathematics
- 2008

We investigate arithmetic properties of the Fourier coefficients of certain harmonic weak Maass forms of weight $1/2$ and $3/2$. Each of the forms in question is the sum of a holomorphic function and…

The spt-function of Andrews

- MathematicsProceedings of the National Academy of Sciences
- 2008

Using another type of identity, one based on Hecke operators, it is obtained a complete multiplicative theory for s(n) modulo 3 and congruences confirm unpublished conjectures of Garvan and Sellers.

HARMONIC MAASS FORMS , MOCK MODULAR FORMS , AND QUANTUM MODULAR FORMS

- Mathematics
- 2012

In his enigmatic death bed letter to Hardy, written in January 1920, Ramanujan introduced the notion of a mock theta function. Despite many works, very little was known about the role that these…

Partition Statistics and Quasiharmonic Maass Forms

- Mathematics
- 2009

Andrews recently introduced k-marked Durfee symbols, which are a generalization of partitions that are connected to moments of Dyson's rank statistic. He used these connections to find identities…

Bringmann, Kathrin and Diamantis, Nikolaos and Raum, Martin (2013) Mock period functions, sesquiharmonic Maass forms, and non-critical values of L-functions. Advances in Mathematics, 233 (1). pp. 115-134. ISSN 0001-8708

- Mathematics
- 2016

. We introduce a new technique of completion for 1-cohomology which parallels the corresponding technique in the theory of mock modular forms. This technique is applied in the context of non-critical…

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