分析中的问题与定理 第2卷
2004-4
北京世界图书出版公司
George Pólya,Gábor Szegő
391
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The present English edition is not a mere translation of the German original. Many new problems have been added and there are also other changes， mostly minor. Yet all the alterations amount to less than ten percent of the text. We intended to keep intact the general plan and the original flavor of the work. Thus we have not introduced any essentially new subject matter， although the mathematical fashion has greatly changed since 1024. We have restricted ours'elves to supplementing the topics originally chosen.
Part Four. Functions of One Complex Variable. Special Part Chapter 1. Maximum Term and Central Index， Maximum Modulus and Number of Zeros Problem Numbers 1 （1-40） Analogy between u（r） and M（r）， v（r） and N （r） 2 （41-47） Further Results on u（r） and v（r） 3 （48-66） Connection between u（r）， v（r）， M（r） and N（r） 4 （67-76） u（r） and M（r） under Special Regularity Assumptions Chapter 2. Sehlicht Mappings 1 （77-83） Introductory Material 2 （84-87） Uniqueness Theorems 3 （88-96） Existence of the Mapping Function 4 （97-120） The Inner and the Outer Radius. The Normed Mapping Function 5 （121-135） Relations between the Mappings of Different Domains 6 （136-163） The Koebe Distortion Theorem and Related Topics Chapter 3. Miscellaneous Problems 1 （164-174.2） Various Propositions 2 （175-179） A Method of E. Landau 3 （180-187） Rectilinear Approach to an Essential Singularity 4 （188-194） Asymptotic Values of Entire Functions 5（195-205）Fulther Applications of the Phragmen-Lindelof Method6 （206-212） Supplementary ProblemsPart Five The Location of Zeros Chapter 1.Rolle'sTheorem and Descartes Rule of SignsChapter 2 The Geometry of the Complex Plane Zeros of PolynomlansChapter 3Miscellaneous ProblemsPart Six.Polynomials and Trigonmetric PolynomialsPart Seven.Determinants and Quadratic FormsPart Eight.Number TheoryChapter 1 Arithmetical FunctionsChapter 2 Polynomials with INtegral Coefficients and Integral-Valued FunctionsChapter 3 Arithmetical Aspects Power SeriesChapter 4 Some Problems on Algebraic IntegersChapter 5 Miscellangous ProblemsPart Nine.Geometric ProblemsAppendix
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