UID:
almafu_9958095308402883
Format:
1 online resource (733 p.)
ISBN:
1-281-79734-0
,
9786611797348
,
0-08-087164-X
Series Statement:
North-Holland mathematics studies ; 53
Content:
Nine Introductions in Complex Analysis
Note:
Description based upon print version of record.
,
Front Cover; Nine Introductions in Complex Analysis; Copyright Page; Table of Contents; Foreword; Chapter I. Conformal Mapping & Riemann Mapping Theorem; I.1 Introduction; I.2 Linear Fractional Transformations; I.3 Univalent Functions; I.4 Normal Families; I.5 The Riemann Mapping Theorem; Chapter II. Picard's Theorems; II.1 The Bloch-Landau Approach; II.2 The Elliptic Modular Function; II.3 The Constants of Bloch and Landau; Chapter III. An Introduction to Entire Functions; III.1 Growth, Order, and Zeros; III.2 Growth, Coefficients and Type; III.3 The Phragmen-Lindelof Indicator
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III.4 Composition of Entire FunctionsChapter IV. Introduction to Meromorphic Functions; IV.1 Nevanlinna's Characteristics and its Elementary Properties; IV.2 Nevanlinna's Second Fundamental Theorem; IV.3 Nevanlinna's Second Fundamental Theorem: Some Applications; Chapter V. Asymptotic Values; V.1 Julia's Theorem; V.2 The Denjoy-Carleman-Ahlfors Theorem; Chapter VI. Natural Boundaries; VI.1 Natural Boundaries--Some Examples; VI.2 The Hadamard Gap Theorem and Over-convergence; VI.3 The Hadamard Multiplication Theorem; VI.4 The Fabry Gap Theorem; VI.5 The Polya-Carlson Theorem
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Chapter VII. The Bieberbach ConjectureVII.1 Elementary Area and Distortion Theorems; VII.2 Some Coefficient Theorems; Chapter VIII. Elliptic Functions; VIII.1 Elementary Properties; VIII.2 Weierstrass' P-function; VIII.3 Weierstrass' t-and a-functions; VIII.4 Jacobi's Elliptic Functions; VIII.5 Theta Functions; VIII.6 Modular Functions; Chapter IX. Introduction to the Riemann Zeta-Function; IX.1 Prime Numbers and t(s); IX.2 Ordinary Dirichlet Series; IX.3 The Functional Equation, the Prime Number Theorem, and De la Vallee-Poussin's Estimate; IX.4 The Riemann Hypothesis; Appendix
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I The Area TheoremII The Borel-Caratheodory Lemma; III The Schwarz Reflection Principle; IV A Special Case of the Osgood-Caratheodory Theorem; V Farey Series; VI The Hadamard Three Circles Theorem; VII The Poisson Integral Theorem; VIII Bernoulli Numbers; IX The Poisson Summation Formula; X The Fourier Integral Theorem; Word List; Bibliographic Remarks
,
English
Additional Edition:
ISBN 0-444-86226-9
Language:
English
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