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

  • Dongxi YeEmail author
Article
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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.

Keywords

Automorphic Green functions Fuchsian subgroups weakly holomorphic modular functions 

Mathematics Subject Classification

11F03 11F11 11F37 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematics (Zhuhai)Sun Yat-sen UniversityZhuhaiPeople’s Republic of China

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