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Identities of Exponential Functions

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Entire and Meromorphic Functions

Part of the book series: Universitext ((UTX))

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Abstract

In this chapter, which is based on [13], we take up some questions prompted by mathematical logic, notably Tarski’s “High School Algebra Problem.” We study identities between certain functions of many variables that are constructed by using the elementary functions of addition x + y, multiplication x• y, and one-place exponentiation ex, starting out with all the complex constants and the independent variables z 1,…, z n. We show that every true identity in this class follows from the natural set of 11 axioms of High School Algebra. The major tool in our proofs is the Nevanlinna theory of entire functions of n complex variables, of which we give a brief sketch. It is entirely parallel to the one-variable theory presented in detail earlier in this book. The timid reader can take n = 1, at least for a first reading.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois, Urbana-Champaign, Urbana, IL, 61801-2917, USA

    Lee A. Rubel & James E. Colliander

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  1. Lee A. Rubel
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  2. James E. Colliander
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© 1996 Springer Science+Business Media New York

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Rubel, L.A., Colliander, J.E. (1996). Identities of Exponential Functions. In: Entire and Meromorphic Functions. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0735-1_24

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  • DOI: https://doi.org/10.1007/978-1-4612-0735-1_24

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94510-1

  • Online ISBN: 978-1-4612-0735-1

  • eBook Packages: Springer Book Archive

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