Research Problems in Function Theory

1. Front Matter

   Pages i-viii

   PDF

2. Meromorphic Functions

   • Walter K. Hayman, Eleanor F. Lingham

   Pages 1-22

3. Entire Functions

   • Walter K. Hayman, Eleanor F. Lingham

   Pages 23-61

4. Subharmonic and Harmonic Functions

   • Walter K. Hayman, Eleanor F. Lingham

   Pages 63-79

5. Polynomials

   • Walter K. Hayman, Eleanor F. Lingham

   Pages 81-95

6. Functions in the Unit Disc

   • Walter K. Hayman, Eleanor F. Lingham

   Pages 97-131

7. Univalent and Multivalent Functions

   • Walter K. Hayman, Eleanor F. Lingham

   Pages 133-184

8. Miscellaneous

   • Walter K. Hayman, Eleanor F. Lingham

   Pages 185-216

9. Spaces of Functions

   • Walter K. Hayman, Eleanor F. Lingham

   Pages 217-229

10. Interpolation and Approximation

    • Walter K. Hayman, Eleanor F. Lingham

    Pages 231-240

11. Back Matter

    Pages 241-284

    PDF

In 1967 Walter K. Hayman published ‘Research Problems in Function Theory’, a list of 141 problems in seven areas of function theory. In the decades following, this list was extended to include two additional areas of complex analysis, updates on progress in solving existing problems, and over 520 research problems from mathematicians worldwide. It became known as ‘Hayman's List’.

This Fiftieth Anniversary Edition contains the complete ‘Hayman's List’ for the first time in book form, along with 31 new problems by leading international mathematicians. This list has directed complex analysis research for the last half-century, and the new edition will help guide future research in the subject. The book contains up-to-date information on each problem, gathered from the international mathematics community, and where possible suggests directions for further investigation.

Aimed at both early career and established researchers, this book provides the key problems andresults needed to progress in the most important research questions in complex analysis, and documents the developments of the past 50 years.

• Hayman's List
• Nevanlinna theory
• Function theory
• Research problems
• Walter Hayman

“This book is superbly written, it is a pleasure to read, and it will surely prove to be an indispensable tool for all researchers interested in function theory. … This up-to-date list of problems will surely keep function theorists intrigued for further 50 years or more.” (Risto Korhonen, zbMATH 1455.30002, 2021)

“It is an absorbing, indeed addictive, volume for anyone interested in complex variables. … I encourage every reader of this review to get a copy of this wonderful book.” (Christopher Bishop, Mathematical Reviews, June, 2020)

• Department of Mathematics, Imperial College London, London, UK

  Walter K. Hayman

• Department of Engineering and Mathematics, Sheffield Hallam University, Sheffield, UK

  Eleanor F. Lingham

Walter K. Hayman is an Emeritus Professor at Imperial College London. The author of five influential books, he is best known for his fundamental work on the theory of functions. Over the course of his career, he has made many outstanding contributions to the study of functions of a complex variable, notably providing solutions to some of the most famous problems in the field. Foremost amongst these is the so-called asymptotic Bieberbach conjecture, for which he provided a definitive proof in 1955. With Margaret Hayman, he founded the British Mathematical Olympiad. He was elected to the Royal Society in 1956, earlier than any other living member bar one (Freeman Dyson). The author of over 200 scientific papers, Walter has won many of the most prestigious accolades in his field and has received honorary degrees from universities in four countries.

Eleanor F. Lingham is a Senior Lecturer at Sheffield Hallam University. She studied for her undergraduate and Masters degrees at University College Cork, and for her PhD at the University of Nottingham.

Policies and ethics