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Infinite Entropy for Transcendental Entire Functions with an Omitted Value

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Abstract

We prove that entire transcendental holomorphic functions with an omitted value have infinite entropy. A proof for general transcendental entire functions will be given in an upcoming paper.

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Funding

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 703269 COTRADY. The second author is supported by the NFR grant no. 240569.

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Authors and Affiliations

  1. Departamento de Matemáticas y Informática, Universitat de Barcelona, Barcelona, Spain

    Anna Miriam Benini

  2. Department of Mathematical Sciences, NTNU Trondheim, Trondheim, Norway

    John Erik Fornæss

  3. Korteweg de Vries Institute for Mathematics, University of Amsterdam, Amsterdam, The Netherlands

    Han Peters

Authors
  1. Anna Miriam Benini
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  2. John Erik Fornæss
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  3. Han Peters
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Corresponding author

Correspondence to Anna Miriam Benini.

Additional information

Dedicated to Lê Văn Thiêm on the occasion of his centenary

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Benini, A.M., Fornæss, J.E. & Peters, H. Infinite Entropy for Transcendental Entire Functions with an Omitted Value. Acta Math Vietnam 45, 49–52 (2020). https://doi.org/10.1007/s40306-018-0300-1

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  • DOI: https://doi.org/10.1007/s40306-018-0300-1

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