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Complex Analysis 2 Pt.2

Riemann Surfaces, Several Complex Variables, Abelian Functions, Higher Modular Functions
BuchKartoniert, Paperback
506 Seiten
Englisch
Springererschienen am29.06.20112. Aufl.
The book contains a complete self-contained introduction to highlights of classical complex analysis. New proofs and some new results are included. All needed notions are developed within the book: with the exception of some basic facts which can be found in the ¯rst volume. There is no comparable treatment in the literature.mehr
Verfügbare Formate
BuchKartoniert, Paperback
EUR74,89
E-BookPDF1 - PDF WatermarkE-Book
EUR85,59

Produkt

KlappentextThe book contains a complete self-contained introduction to highlights of classical complex analysis. New proofs and some new results are included. All needed notions are developed within the book: with the exception of some basic facts which can be found in the ¯rst volume. There is no comparable treatment in the literature.
ZusammenfassungThis extensive description of classical complex analysis omits sheaf theoretical and cohomological methods to focus on the full quota of essential concepts related to the topic. Lots of exercises and figures make it an ideal introduction to the subject.
Details
ISBN/GTIN978-3-642-20553-8
ProduktartBuch
EinbandartKartoniert, Paperback
Verlag
Erscheinungsjahr2011
Erscheinungsdatum29.06.2011
Auflage2. Aufl.
ReiheUniversitext
Seiten506 Seiten
SpracheEnglisch
Gewicht760 g
IllustrationenXIII, 506 p. 51 illus.
Artikel-Nr.10386950

Inhalt/Kritik

Inhaltsverzeichnis
Chapter I. Riemann Surfaces.- Chapter II. Harmonic Functions on Riemann Surfaces.- Chapter III. Uniformization.- Chapter IV. Compact Riemann Surfaces.- Appendices to Chapter IV.- Chapter V. Analytic Functions of Several Complex Variables.- Chapter V. Analytic Functions of Several Complex Variable.- Chapter VI. Abelian Functions.- Chapter VII. Modular Forms of Several Variables.- Chapter VIII. Appendix: Algebraic Tools.- References.- Index.mehr
Kritik
From the reviews:

"The book under review is the second volume of the textbook Complex analysis, consisting of 8 chapters. It provides an approach to the theory of Riemann surfaces from complex analysis. ... The book is self-contained and, moreover, some notions which might be unfamiliar for the reader are explained in appendices of chapters. ... this book is an excellent textbook on Riemann surfaces, especially for graduate students who have taken the first course of complex analysis." (Hiroshige Shiga, Mathematical Reviews, Issue 2012 f)

"The book under review is largely self-contained, pleasantly down-to-earth, remarkably versatile, and highly educating simultaneously. No doubt, this fine textbook provides an excellent source for the further study of more advanced and topical themes in the theory of Riemann surfaces, their Jacobians and moduli spaces, and in the general theory of complex Abelian varieties and modular forms likewise. It is very welcome that the English translation of the German original has been made available so quickly!" (Werner Kleinert, Zentralblatt MATH, Vol. 1234, 2012)

"The author provides a (very brief) introduction to fundamental notions of topology, but develops fully the theory of surfaces and covering spaces he needs. ... the book includes a proof of the classification of compact orientable surfaces by their genus. ... this one is definitely a graduate text. ... There is a lot of mathematics in this book, presented efficiently and well. ... It is a book I am glad to have, and that I will certainly refer to in the future." (Fernando Q. Gouvêa, The Mathematical Association of America, May, 2012)mehr