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An analogue of Weil’s converse theorem for harmonic Maass forms of polynomial growth

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Abstract

We construct a family of harmonic Maass forms of polynomial growth of any level corresponding to any cusp whose shadows are Eisenstein series of integral weight. We further consider Dirichlet series attached to a harmonic Maass form of polynomial growth, study its analytic properties, and prove an analogue of Weil’s converse theorem.

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Acknowledgements

We would like to thank the anonymous referees for detailed comments and suggestions which led to some mathematical corrections and an improvement of the presentation.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Science Education and Research Bhopal, Bhopal Bypass Road, Bhauri, Bhopal, Madhya Pradesh, 462 066, India

    Karam Deo Shankhadhar

  2. NHETC, Department of Physics and Astronomy, Rutgers University, 126 Frelinghuysen Rd., Piscataway, NJ, 08855, USA

    Ranveer Kumar Singh

Authors
  1. Karam Deo Shankhadhar
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  2. Ranveer Kumar Singh
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Correspondence to Karam Deo Shankhadhar.

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Shankhadhar, K.D., Singh, R.K. An analogue of Weil’s converse theorem for harmonic Maass forms of polynomial growth. Res. number theory 8, 36 (2022). https://doi.org/10.1007/s40993-022-00334-9

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