Completely replicable functions and symmetries
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Completely replicable functions play an important role in number theory and finite group theory, in particular the Monstrous Moonshine. In this paper, we give a characterization of completely replicable functions by certain symmetries.
KeywordsCompletely replicable functions Faber polynomials Symmetries
Mathematics Subject Classification11F03 11F12 11F22
The authors would like to thank the referee for carefully reading our manuscript and for giving valuable suggestions. The first author thanks the Max Planck Institute for Mathematics for support and an invitation in July and August 2017. He also thanks Kyoto Sangyo University and Professor Murase for an invitation in January 2018 to extend our collaboration. He also thanks Prof. Krieg for useful discussions at the Graduate school: Experimental and constructive algebra, at the RWTH Aachen in 2018 and the German University of Technology in Oman for work leave. The second author is partially supported by Grants-in-Aids from JSPS (17K05186).
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