IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-0348-7121-1_6.html
   My bibliography  Save this book chapter

Recent Progress in Nevanlinna’s Theory of Meromorphic Functions

In: Zum Werk Leonhard Eulers

Author

Listed:
  • Albert Baernstein II

    (Washington University, Department of Mathematics)

Abstract

We shall consider meromorphic functions f defined in the whole complex plane C. If f is a rational function of degree n then f takes on every value a ∈ C*= C u {∞} exactly n times when account is taken of multiplicities and the behavior of f at ∞. When f is transcendental Picard’s theorem (1879) asserts that f takes on every value a ∈ C* infinitely often, with at most two possible exceptions. The exponential function f(z) = ez omits a = O and a = ∞, thus showing that two exceptional values are possible. Since Euler played an important role in the development of ez, we may regard him as one of the important contributions to our subject.

Suggested Citation

  • Albert Baernstein II, 1984. "Recent Progress in Nevanlinna’s Theory of Meromorphic Functions," Springer Books, in: Eberhard Knobloch & Ilppo Simo Louhivaara & Jörg Winkler (ed.), Zum Werk Leonhard Eulers, pages 121-131, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-7121-1_6
    DOI: 10.1007/978-3-0348-7121-1_6
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-0348-7121-1_6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.