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Bases of spaces of harmonic weak Maass forms and Shintani lifts of harmonic weak Maass forms

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Abstract

We construct bases of the space of harmonic weak Maass forms of weight \(\kappa \in \frac{1}{2}{\mathbb {Z}}\). Using these bases, we obtain a Shintani lift from a positive integral weight harmonic weak Maass form to a half-integral weight harmonic weak Maass form, which reduces to the classical Shintani lift on the space of cusp forms.

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Authors and Affiliations

  1. Department of Mathematics Education, Kongju National University, Gongju, 32588, Korea

    Daeyeol Jeon

  2. Department of Mathematics, Kangwon National University, Chuncheon, 24341, Korea

    Soon-Yi Kang

  3. Department of Mathematics, Sungkyunkwan University, Suwon, 16419, Korea

    Chang Heon Kim

Authors
  1. Daeyeol Jeon
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  2. Soon-Yi Kang
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  3. Chang Heon Kim
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Correspondence to Chang Heon Kim.

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Daeyeol Jeon was supported by the National Research Foundation of Korea (NRF) grant (NRF-2016R1D1A1B03934504). Soon-Yi Kang was supported by the NRF grant (NRF-2016R1D1A1B01012258). Chang Heon Kim was supported by the NRF grant (NRF-2018R1D1A1B07045618 and 2016R1A5A1008055)

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Jeon, D., Kang, SY. & Kim, C.H. Bases of spaces of harmonic weak Maass forms and Shintani lifts of harmonic weak Maass forms. Ramanujan J 54, 219–244 (2021). https://doi.org/10.1007/s11139-019-00197-2

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  • DOI: https://doi.org/10.1007/s11139-019-00197-2

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