Experimental Mathematics

Computation of Harmonic Weak Maass Forms

Jan H. Bruinier and Fredrik Strömberg

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Harmonic weak Maass forms of half-integral weight have been the subject of much recent work. They are closely related to Ramanujan’s mock theta functions, and their theta lifts give rise to Arakelov Green functions, and their coefficients are often related to central values and derivatives of Hecke L-functions. We present an algorithm to compute harmonic weak Maass forms numerically, based on the automorphymethod due to Hejhal and Stark. As explicit examples we consider harmonic weak Maass forms of weight 1/2 associated to the elliptic curves 11a1, 37a1, 37b1. We have made extensive numerical computations, and the data we obtained are presented in this paper. We expect that experiments based on our data will lead to a better understanding of the arithmetic properties of the Fourier coefficients of harmonic weak Maass forms of half-integral weight.

Article information

Experiment. Math., Volume 21, Issue 2 (2012), 117-131.

First available in Project Euclid: 31 May 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11Y35: Analytic computations 11Y40: Algebraic number theory computations 11F30: Fourier coefficients of automorphic forms 11G05: Elliptic curves over global fields [See also 14H52]

Modular form harmonic Maass form elliptic curve L-function Weil representation


Bruinier, Jan H.; Strömberg, Fredrik. Computation of Harmonic Weak Maass Forms. Experiment. Math. 21 (2012), no. 2, 117--131. https://projecteuclid.org/euclid.em/1338430825

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