Complex Analysis Reading List

Here is a list of few books dealing with complex analysis and related ideas. It is not a comprehensive list. It just happens to be what I had conveniently available when I made the list. From time to time I may refer to some of them. I expect that you may find [10], [11], [37], [9] and [1] most useful for Mth 514/5/6.

I recommend you look at [31] even though it is not particularly well suited for our Complex Analysis course. It is an exceptionally interesting and entertaining book from which you can learn a great deal about complex analysis.

[1]

Mark J. Ablowitz and Athanassios S. Fokas, Complex variable. Introduction and applications, Cambridge University Press, Cambridge, New York, Melbourne, 1997.

[2]

Lars. V. Ahlfors, Complex analysis, 2nd ed., McGraw-Hill, New York, St. Louis, San Francisco, Toronto, London, Sydney, 1966.

[3]

____ , Complex analysis, 3rd ed., McGraw-Hill, New York, 1979.

[4]

Sheldon Axler, Paul Bourdon, and Wade Ramey, Harmonic function theory, Springer-Verlag, New York, Brlin, 1992, homelib.

[5]

Joseph Bak and Donald J. Newman, Complex analysis, 2nd ed., Springer-Verlag, New York, Berlin, Heidelbrg, 1997.

[6]

Carlos A. Berenstein and Roger Gay, Complex analysis and special topics in harmonic analysis, Springer-Verlag, New York, Berlin, Heidelberg, 1995.

[7]

Lipman Bers, Introduction to several complex variables. Lecture notes 1962-1963, Courant Institute of Mathematical Sciences. New York Univ., New York, 1964.

[8]

Ralph Philip Boas, Entire functions, Academic Press, New York, 1954.

[9]

____ , Invitation to complex analysis, Random House, New York, 1987.

[10]

John B. Conway, Functions of one complex variable, 2nd ed., Graduate Texts in Mathematics, vol. 11, Springer-Verlag, New York, Berlin, Heidelberg, London, Paris, Tokyo, Hong Kong, Barcelona, 1978.

[11]

John Hamilton Curtiss, Introduction to functions of a complex variable, Marcel Dekker, New York, Basel, 1978.

[12]

Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1965.

[13]

Maurice Heins, Selected topics in the classical theory of functions of a complex variable, Holt, Rinehart and Winston, New York, 1962.

[14]

____ , Complex function theory, Academic Press, New York and London, 1968.

[15]

Einar Hille, Analytic function theory, vol. 1, Ginn and Co., Boston, New York, Chicago, Atlanta, Dallas, Palo Alto, Toronto, London, 1959.

[16]

____ , Analytic function theory, vol. 2, Ginn and Co., Boston, New York, Chicago, Atlanta, Dallas, Palo Alto, Toronto, 1962.

[17]

Lars Hörmander, An introduction to complex analysis in several variables, D. van Nostrand Co., Inc., Princeton, New Jersey, Toronto, New York, London, 1966.

[18]

Aleksandar Ivi\'c, The Riemann zeta-function. The theory of the riemann zeta-function with applications, John Wiley & Sons, New York, 1985.

[19]

Alan Jeffrey, Complex analysis and applications, CRC Press, Boca Raton, Ann Arbor, London, 1992.

[20]

Gareth A. Jones and David Singerman, Complex functions. An algebraic and geometric viewpoint, Cambridge University Press, Cambridge, New York, Port Chester, Melbourne, Sydney, 1987.

[21]

Konrad Knopp, Theory of functions, Part I, Dover Publ., New York, 1945 (Translated from German fifth ed. by Frederick Bagemihl).

[22]

____ , Theory of functions, Part II, Dover Publ., New York, 1947 (Translated from German fourth ed. by Frederick Bagemihl).

[23]

____ , Problem book in the theory of functions, vol. 1, Dover Publ., New York, 1948 (Translated from German by Lipman Bers).

[24]

____ , Elements of the theory of functions, Dover Publ., New York, 1952 (Translated from German by Frederick Bagemihl).

[25]

____ , Problem book in the theory of functions, vol. 2, Dover Publ., New York, 1952 (Translated from German by Frederick Bagemihl).

[26]

Steven G. Krantz, Function theory of several complex variables, John Wiley & Sons, New York, Chichester, Brisbane, Toronto, Singapore, 1982.

[27]

Norman Levinson and Raymond M. Redheffer, Complex variables, Holden-Day, Inc., San Francisco, Cambridge, London, Amsterdam, 1970.

[28]

John H. Mathews and Russell W. Howell, Complex analysis for mathematics and engineering, 3rd ed., Jones and Bartlett, Sudbury-Massachusetts, Boston, London, Singapore, 1997.

[29]

Raghavan Narasimhan, Several complex variable, University of Chicago Press, Chicago, London, 1971.

[30]

S. J. Patterson, An introduction to the theory of the Riemann zeta-function, Cambridge Univ. Press, Cambridge New York Melbourne, 1988.

[31]

Reinhold Remmert, Theory of complex functions, Graduate Texts in Mathematics, Readings in Mathematics , vol. 122, Springer-Verlag, New York, Berlin, Heidelberg, London, Paris, Tokyo, Hong Kong, 1991 (Translated from 2nd German edition of Funktionentheorie I , Grundwissen Mathematik, vol. 5, 1989).

[32]

Walter Rudin, Real and complex analysis, 2nd ed., McGraw-Hill, New York, St. Louis, San Francisco, 1974.

[33]

Georg Evgen'evich Shilov, Elementary real and complex analysis, The MIT Press, Cambridge, Massachusetts, London, England, 1973 (Translated from Russian and revised).

[34]

Kennan T. Smith, Power series from a computational point of view, Springer-Verlag, New York, Berlin, Heidelberg, London, Paris, Tokyo, 1987.

[35]

E. C. Titchmarsh, The zeta-function of Riemann, Cambridge Tracts in Mathematics and Mathematical Physics, no. 26, Cambridge Univ. Press, London, 1930.

[36]

____ , The theory of functions, Oxford Univ. Press, Oxford, 1932.

[37]

____ , The theory of functions, 2nd ed., Oxford Univ. Press, Oxford, 1939.

[38]

____ , The theory of the Riemann zeta-function, Oxford Univ. Press, London, Glascow, New York, 1951.

[39]

L. I. Volkovyskii, G. L. Lunts, and I. G. Aramanovich, A collection of problems on complex analysis, Dover Publications, Inc., New York, 1991 (Republication of Pergamon Press edition of 1965, translation of original Russian Fizmatgiz edition of 1960).

petersen@math.oregonstate.edu

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