Entire and Meromorphic Functions

• 1. Introduction.- 2. The Riemann-Stieltjes Integral.- 3. Jensen’s Theorem and Applications.- 4. The First Fundamental Theorem of Nevanlinna Theory.- 5. Elementary Properties of T(r,f).- 6. The Cartan Formulation of the Characteristic.- 7. The Poisson-Jensen Formula.- 8. Applications of T(r).- 9. A Lemma of Borel and Some Applications.- 10. The Maximum Term of an Entire Function.- 11. Relation Between the Growth of an Entire Function and the Size of Its Taylor Coefficients.- 12. Carleman’s Theorem.- 13. A Fourier Series Method.- 14. The Miles-Rubel-Taylor Theorem on Quotient Representations of Meromorphic Functions.- 15. Canonical Products.- 16. Formal Power Series.- 17. Picard’s Theorem and the Second Fundamental Theorem.- 18. A Proof of the Second Fundamental Theorem.- 19. “Two Constant” Theorems and the Phragmén-Lindelöf Theorems.- 20. The Pólya Representation Theorem.- 21. Integer-Valued Entire Functions.- 22. On Small Entire Functions of Exponential-Type with Given Zeros.- 23. The First-Order Theory of the Ring of All Entire Functions.- 24. Identities of Exponential Functions.- References.

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)