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On the Generating Function of a Canonical Basis for \({\varvec{M_{0}^{!,\infty }(\Gamma )}}\)

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Abstract

In this note, we use automorphic Green functions to show that the generating function of a canonical basis for the space of weakly holomorphic modular functions with poles supported at the cusp \(i\infty \) for a Fuchsian subgroup of the first kind of genus zero has a weight 2 meromorphic modular form representation.

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Acknowledgements

The author thanks Professor Tonghai Yang for his encouragement and fruitful discussion. The author would also like to thank the anonymous referee for his/her helpful comments, suggestions and corrections, and in particular, for the information in Remark 2.2.

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  1. School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai, 519082, Guangdong, People’s Republic of China

    Dongxi Ye

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  1. Dongxi Ye
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Correspondence to Dongxi Ye.

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This work was partially supported by an NSF Grant DMS-1500743.

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Ye, D. On the Generating Function of a Canonical Basis for \({\varvec{M_{0}^{!,\infty }(\Gamma )}}\). Results Math 74, 72 (2019). https://doi.org/10.1007/s00025-019-1001-3

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  • DOI: https://doi.org/10.1007/s00025-019-1001-3

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