JournalsjemsVol. 22, No. 4pp. 1115–1148

Harmonic Maass forms associated to real quadratic fields

  • Pierre Charollois

    Sorbonne Université, Université Paris 6, France

  • Yingkun Li

    Technische Universität Darmstadt, Germany
Harmonic Maass forms associated to real quadratic fields cover

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Abstract

In this paper, we explicitly construct harmonic Maass forms that map to the holomorphic weight 1 theta series associated by Hecke to odd ray class group characters of real quadratic fields. From this construction, we give precise arithmetic information contained in the Fourier coefficients of the holomorphic part of the harmonic Maass form, establishing the main part of a conjecture of the second author.

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Cite this article

Pierre Charollois, Yingkun Li, Harmonic Maass forms associated to real quadratic fields. J. Eur. Math. Soc. 22 (2020), no. 4, pp. 1115–1148

DOI 10.4171/JEMS/941