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

  • Dongxi YeEmail author


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.


Automorphic Green functions Fuchsian subgroups weakly holomorphic modular functions 

Mathematics Subject Classification

11F03 11F11 11F37 



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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© 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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