# Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms

@article{Bruinier2011AlgebraicFF, title={Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms}, author={Jan H. Bruinier and Ken Ono}, journal={Advances in Mathematics}, year={2011}, volume={246}, pages={198-219} }

## 89 Citations

Singular invariants and coefficients of harmonic weak Maass forms of weight 5/2

- Mathematics
- 2016

Abstract We study the coefficients of a natural basis for the space of harmonic weak Maass forms of weight 5 / 2 ${5/2}$ on the full modular group. The non-holomorphic part of the first element of…

Singular invariants and coefficients of weak harmonic Maass forms of weight 5/2

- Mathematics
- 2014

We study the coefficients of a natural basis for the space of weak harmonic Maass forms of weight $5/2$ on the full modular group. The non-holomorphic part of the first element of this infinite basis…

Fourier coefficients of harmonic weak Maass forms and the partition function

- Mathematics
- 2015

In a recent paper, Bruinier and Ono proved that certain harmonic weak Maass forms have the property that the Fourier coefficients of their holomorphic parts are algebraic traces of weak Maass forms…

CM values and Fourier coefficients of harmonic Maass forms

- Mathematics
- 2015

In this thesis, we show that the Fourier coefficients of certain half-integral weight harmonic Maass forms are given as ``twisted traces'' of CM values of integral weight harmonic Maass forms. These…

Computation of Harmonic Weak Maass Forms

- MathematicsExp. Math.
- 2012

This paper presents an algorithm to compute harmonic weak Maass forms numerically, based on the automorphy method due to Hejhal and Stark, and expects that experiments based on its data will lead to a better understanding of the arithmetic properties of the Fourier coefficients of harmonic weakMaass forms of half-integrals.

Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function

- Mathematics
- 2013

We construct a natural basis for the space of weak harmonic Maass forms of weight 5/2 on the full modular group. The nonholomorphic part of the first element of this basis encodes the values of the…

Locally Harmonic Maass Forms and the Kernel of the Shintani Lift

- Mathematics
- 2012

In this paper we define a new type of modular object and construct explicit examples of such functions. Our functions are closely related to cusp forms constructed by Zagier [37] which played an…

Arithmetic properties of Fourier coefficients of meromorphic modular forms

- MathematicsAlgebra & Number Theory
- 2021

We investigate integrality and divisibility properties of Fourier coefficients of meromorphic modular forms of weight $2k$ associated to positive definite integral binary quadratic forms. For…

Singular moduli and the distribution of partition ranks modulo 2

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 2015

Abstract In this paper, we prove an asymptotic formula with a power saving error term for traces of weight zero weakly holomorphic modular forms of level N along Galois orbits of Heegner points on…

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Recently, Bruinier and Ono proved that the coefficients of certain weight $$-1/2$$-1/2 harmonic weak Maaß forms are given as “traces” of singular moduli for harmonic weak Maaß forms. Here, we prove…

Cycle integrals of the j-function and mock modular forms

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