Skip to main content
  • Textbook
  • © 1996

Entire and Meromorphic Functions

Part of the book series: Universitext (UTX)

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

This is a preview of subscription content, log in via an institution to check for access.

Table of contents (24 chapters)

  1. Front Matter

    Pages i-viii
  2. Introduction

    • Lee A. Rubel, James E. Colliander
    Pages 1-2
  3. The Riemann-Stieltjes Integral

    • Lee A. Rubel, James E. Colliander
    Pages 3-5
  4. Jensen’s Theorem and Applications

    • Lee A. Rubel, James E. Colliander
    Pages 6-8
  5. The First Fundamental Theorem of Nevanlinna Theory

    • Lee A. Rubel, James E. Colliander
    Pages 9-11
  6. Elementary Properties of T(r, f)

    • Lee A. Rubel, James E. Colliander
    Pages 12-15
  7. The Cartan Formulation of the Characteristic

    • Lee A. Rubel, James E. Colliander
    Pages 16-19
  8. The Poisson-Jensen Formula

    • Lee A. Rubel, James E. Colliander
    Pages 20-22
  9. Applications of T(r)

    • Lee A. Rubel, James E. Colliander
    Pages 23-25
  10. A Lemma of Borel and Some Applications

    • Lee A. Rubel, James E. Colliander
    Pages 26-29
  11. The Maximum Term of an Entire Function

    • Lee A. Rubel, James E. Colliander
    Pages 30-39
  12. Carleman’s Theorem

    • Lee A. Rubel, James E. Colliander
    Pages 45-48
  13. A Fourier Series Method

    • Lee A. Rubel, James E. Colliander
    Pages 49-77
  14. Canonical Products

    • Lee A. Rubel, James E. Colliander
    Pages 87-92
  15. Formal Power Series

    • Lee A. Rubel, James E. Colliander
    Pages 93-98
  16. Picard’s Theorem and the Second Fundamental Theorem

    • Lee A. Rubel, James E. Colliander
    Pages 99-112
  17. A Proof of the Second Fundamental Theorem

    • Lee A. Rubel, James E. Colliander
    Pages 113-120
  18. “Two Constant” Theorems and the Phragmén-Lindelöf Theorems

    • Lee A. Rubel, James E. Colliander
    Pages 121-123

About this book

Mathematics is a beautiful subject, and entire functions is its most beautiful branch. Every aspect of mathematics enters into it, from analysis, algebra, and geometry all the way to differential equations and logic. For example, my favorite theorem in all of mathematics is a theorem of R. NevanJinna that two functions, meromorphic in the whole complex plane, that share five values must be identical. For real functions, there is nothing that even remotely corresponds to this. This book is an introduction to the theory of entire and meromorphic functions, with a heavy emphasis on Nevanlinna theory, otherwise known as value-distribution theory. Things included here that occur in no other book (that we are aware of) are the Fourier series method for entire and mero­ morphic functions, a study of integer valued entire functions, the Malliavin­ Rubel extension of Carlson's Theorem (the "sampling theorem"), and the first-order theory of the ring of all entire functions, and a final chapter on Tarski's "High School Algebra Problem," a topic from mathematical logic that connects with entire functions. This book grew out of a set of classroom notes for a course given at the University of Illinois in 1963, but they have been much changed, corrected, expanded, and updated, partially for a similar course at the same place in 1993. My thanks to the many students who prepared notes and have given corrections and comments.

Reviews

From the reviews:

"This book grew out of lectures from courses given at the University of Illinois in 1993, and earlier. It is written at a level which assumes only a reasonable first course in complex analysis and knowledge of some standard results about the representation of linear functionals....The book is divided into 24 relatively short chapters, and, although some of the later material depends on earlier material, the reader who already has some knowledge of the general subject from other sources should be able to go directly to one of the later sections of the book without undue difficulties.

This book is a very welcome addition to the resources available for learning about entire and meromorphic functions."  (P. Lappan, Mathematical Reviews) 

Authors and Affiliations

  • Department of Mathematics, University of Illinois, Urbana-Champaign, Urbana, USA

    Lee A. Rubel, James E. Colliander

Bibliographic Information

  • Book Title: Entire and Meromorphic Functions

  • Authors: Lee A. Rubel, James E. Colliander

  • Series Title: Universitext

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

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1996

  • Softcover ISBN: 978-0-387-94510-1Published: 28 February 1996

  • eBook ISBN: 978-1-4612-0735-1Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: VIII, 188

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Analysis

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access