Completely replicable functions and symmetries

  • Bernhard Heim
  • Atsushi MuraseEmail author


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.


Completely replicable functions Faber polynomials Symmetries 

Mathematics Subject Classification

11F03 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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Copyright information

© The Author(s), under exclusive licence to Mathematisches Seminar der Universität Hamburg 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Science, Faculty of ScienceGerman University of Technology in OmanMuscatSultanate of Oman
  2. 2.Faculty of ScienceKyoto Sangyo UniversityKita-kuJapan

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