Abstract
In this note we extend integral weight harmonic Maass forms to functions defined on the upper and lower half-planes using the method of Poincaré series. This relates to Rademacher’s “expansion of zero” principle, which was recently employed by Rhoades to link mock theta functions and partial theta functions.
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Acknowledgements
The research of the second author is supported by the Alfried Krupp Prize for Young University Teachers of the Krupp foundation and the research leading to these results receives funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007–2013)/ERC Grant agreement n. 335220—AQSER.
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Andersen, N., Bringmann, K., Rolen, L. (2017). Images of Maass-Poincaré Series in the Lower Half-Plane. In: Bruinier, J., Kohnen, W. (eds) L-Functions and Automorphic Forms. Contributions in Mathematical and Computational Sciences, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-69712-3_2
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DOI: https://doi.org/10.1007/978-3-319-69712-3_2
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