Analytic Functions of Several Complex Variables

Carl L. Siegel

Kendrick Press, Inc. (2008) viii + 174 pp.
Paperback $70.00. ISBN 0-9793183-7-8

Carl L. Siegel (1896-1981) was one of the finest mathematicians of the twentieth century. The present book is a set of lectures on favorite themes of Siegel, delivered at the Institute for Advanced Study in 1948-1949. The notes on which the book was based were drawn up with great care by Paul T. Bateman. The book, which has been unavailable for many years, has been retyped in an attractive modern format.

Chapter headings: 1. Divisibility properties of power series. 2. Cousin’s problems. 3. Two lemmas. 4. Periodic functions. 5. Difference equations. 6. Period relations. 7. Theta functions. 8. The field of abelian functions. 9. An excursion into topology. 10. Automorphic functions. 11. Existence of discontinuous groups. 12. The modular group of degree p.

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