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Kaneko–Zagier type equation for Jacobi forms of index 1

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Abstract

We introduce a certain fourth-order partial differential equation containing one parameter \(k\), related to Jacobi forms of index 1. We show several properties of the equation and give explicit Jacobi-form solutions for suitable \(k\).

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Acknowledgments

The author would like to thank Professor Masanobu Kaneko for valuable comments and carefully reading preliminary manuscripts of this paper. The author also would like to thank Dr. Yuichi Sakai for giving him helpful advice.

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Authors and Affiliations

  1. Graduate School of Mathematics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Tomoya Kiyuna

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  1. Tomoya Kiyuna
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Correspondence to Tomoya Kiyuna.

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Kiyuna, T. Kaneko–Zagier type equation for Jacobi forms of index 1. Ramanujan J 39, 347–362 (2016). https://doi.org/10.1007/s11139-014-9641-0

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  • DOI: https://doi.org/10.1007/s11139-014-9641-0

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