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1.

図書
図書
1. Analytic number theory
Donald J. Newman
出版情報: New York ; Tokyo : Springer, c1998  viii, 76 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 177
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目次情報: 続きを見る
Introduction and dedication
The idea of analytic number theory
The partition function
The Erdos-Fuchs theorem
Sequences without arithmetic progressions
The Waring problem
A "Natural" Proof of the Non-vanishing of L-Series
Simple Analytic Proof of the Prime Number Theorem
Index
Introduction and dedication
The idea of analytic number theory
The partition function
2.

図書
図書
2. Complex analysis. 2nd ed
Joseph Bak, Donald J. Newman
出版情報: New York : Springer-Verlag, c1997  x, 294 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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3.

図書
図書
3. Polynomial approximation
[by] Robert P. Feinerman [and] Donald J. Newman
出版情報: Baltimore : Williams & Wilkins, c1974  viii, 148 p. ; 24 cm
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4.

図書
図書
4. 数学問題ゼミナール
ドナルド・J・ニューマン著 ; 一松信訳
出版情報: 東京 : シュプリンガー・フェアラーク東京, 1985.3  150p ; 21cm
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5.

図書
図書
5. Complex analysis. 3rd ed
Joseph Bak, Donald J. Newman
出版情報: New York : Springer, c2010  xii, 328 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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目次情報: 続きを見る
Preface to the Third Edition
Preface to the Second Edition
The Complex Numbers / 1：
Introduction
The Field of Complex Numbers / 1.1：
The Complex Plane / 1.2：
The Solution of the Cubic Equation / 1.3：
Topological Aspects of the Complex Plane / 1.4：
Stereographic Projection; The Point at Infinity / 1.5：
Exercises
Functions of the Complex Variable z / 2：
Analytic Polynomials / 2.1：
Power Series / 2.2：
Differentiability and Uniqueness of Power Series / 2.3：
Analytic Functions / 3：
Analyticity and the Cauchy-Riemann Equations / 3.1：
Line Integrals and Entire Functions / 3.2：
Properties of the Line Integral / 4.1：
The Closed Curve Theorem for Entire Functions / 4.2：
Properties of Entire Functions / 5：
The Cauchy Integral Formula and Taylor Expansion for Entire Functions / 5.1：
Liouville Theorems and the Fundamental Theorem of Algebra; The Gauss-Lucas Theorem / 5.2：
Newton's Method and Its Application to Polynomial Equations / 5.3：
Properties of Analytic Functions / 6：
The Power Series Representation for Functions Analytic in a Disc / 6.1：
Analytic in an Arbitrary Open Set / 6.2：
The Uniqueness, Mean-Value, and Maximum-Modulus Theorems; Critical Points and Saddle Points / 6.3：
Further Properties of Analytic Functions / 7：
The Open Mapping Theorem; Schwarz' Lemma / 7.1：
The Converse of Cauchy's Theorem: Morera's Theorem; The Schwarz Reflection Principle and Analytic Arcs / 7.2：
Simply Connected Domains / 8：
The General Cauchy Closed Curve Theorem / 8.1：
The Analytic Function log z / 8.2：
Isolated Singularities of an Analytic Function / 9：
Classification of Isolated Singularities; Riemann's Principle and the Casorati-Weierstrass Theorem / 9.1：
Laurent Expansions / 9.2：
The Residue Theorem / 10：
Winding Numbers and the Cauchy Residue Theorem / 10.1：
Applications of the Residue Theorem / 10.2：
Applications of the Residue Theorem to the Evaluation of Integrals and Sums / 11：
Evaluation of Definite Integrals by Contour Integral Techniques / 11.1：
Application of Contour Integral Methods to Evaluation and Estimation of Sums / 11.2：
Further Contour Integral Techniques / 12：
Shifting the Contour of Integration / 12.1：
An Entire Function Bounded in Every Direction / 12.2：
Introduction to Conformal Mapping / 13：
Conformal Equivalence / 13.1：
Special Mappings / 13.2：
Schwarz-Christoffel Transformations / 13.3：
The Riemann Mapping Theorem / 14：
Conformal Mapping and Hydrodynamics / 14.1：
Mapping Properties of Analytic Functions on Closed Domains / 14.2：
Maximum-Modulus Theorems for Unbounded Domains / 15：
A General Maximum-Modulus Theorem / 15.1：
The Phragmén-Lindelöf Theorem / 15.2：
Harmonic Functions / 16：
Poisson Formulae and the Dirichlet Problem / 16.1：
Liouville Theorems for Re f; Zeroes of Entire Functions of Finite Order / 16.2：
Different Forms of Analytic Functions / 17：
Infinite Products / 17.1：
Analytic Functions Defined by Definite Integrals / 17.2：
Analytic Functions Defined by Dirichlet Series / 17.3：
Analytic Continuation; The Gamma and Zeta Functions / 18：
Analytic Continuation of Dirichlet Series / 18.1：
The Gamma and Zeta Functions / 18.3：
Applications to Other Areas of Mathematics / 19：
A Variation Problem / 19.1：
The Fourier Uniqueness Theorem / 19.2：
An Infinite System of Equations / 19.3：
Applications to Number Theory / 19.4：
An Analytic Proof of The Prime Number Theorem / 19.5：
Answers
References
Appendices
Index
Preface to the Third Edition
Preface to the Second Edition
The Complex Numbers / 1：
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