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1.

図書

図書
H.P. McKean, Jr
出版情報: New York : Academic Press, 1969  xiii, 140 p. ; 24 cm
シリーズ名: Probability and mathematical statistics : a series of monographs and textbooks ; 5
2.

図書

図書
K. Itô, H.P. McKean, Jr
出版情報: Berlin : Springer-Verlag, 1974  xiv, 321 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 125
3.

図書

図書
[edited by Joseph B. Keller and Henry P. McKean]
出版情報: Providence, R.I. : American Mathematical Society, 1973  v, 209 p. ; 26 cm
シリーズ名: SIAM-AMS proceedings ; v. 6
4.

図書

図書
by Kiyosi Itô and Henry P. McKean, Jr
出版情報: Berlin : Springer, 1965  xvi, 321 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 125
5.

図書

図書
H. Dym, H.P. McKean
出版情報: New York : Academic Press, 1976  xi, 333 p. ; 24 cm
シリーズ名: Probability and mathematical statistics : a series of monographs and textbooks ; v. 31
6.

図書

図書
H. Dym, H.P. McKean
出版情報: New York : Academic Press, 1972  x, 295 p. ; 24 cm
シリーズ名: Probability and mathematical statistics : a series of monographs and textbooks ; 14
目次情報: 続きを見る
Historical Introduction
Fourier Series
Fourier Integrals
Fourier Integrals and Complex Function Theory
Fourier Series and Integrals on Groups
Additional Reading
Bibliography
Historical Introduction
Fourier Series
Fourier Integrals
7.

図書

図書
Henry McKean, Victor Moll
出版情報: New York : Cambridge University Press, 1997  xiii, 280 p. ; 24 cm
目次情報: 続きを見る
Preface
First Ideas: Complex Manifolds, Riemann Surfaces, and Projective Curves / 1.:
The Riemann Sphere / 1.1:
Complex Manifolds / 1.2:
Rational Functions / 1.3:
Luroth's Theorem / 1.4:
Automorphisms of P[superscript 1] / 1.5:
Spherical Geometry / 1.6:
Finite Subgroups and the Platonic Solids / 1.7:
Automorphisms of the Half-Plane / 1.8:
Hyperbolic Geometry / 1.9:
Projective Curves / 1.10:
Covering Surfaces / 1.11:
Scissors and Paste / 1.12:
Algebraic Functions / 1.13:
Examples / 1.14:
More on Uniformization / 1.15:
Compact Manifolds as Curves: Finale / 1.16:
Elliptic Integrals and Functions / 2.:
Elliptic Integrals: Where They Come From / 2.1:
The Incomplete Integrals Reduced to Normal Form / 2.2:
The Complete Integrals: Landen, Gauss, and the Arithmetic-Geometric Mean / 2.3:
The Complete Elliptic Integrals: Legendre's Relation / 2.4:
The Discovery of Gauss and Abel / 2.5:
Periods in General / 2.6:
Elliptic Functions in General / 2.7:
The and-Function / 2.8:
Elliptic Integrals, Complete and Incomplete / 2.9:
Two Mechanical Applications / 2.10:
The Projective Cubic / 2.11:
The Problem of Inversion / 2.12:
The Function Field / 2.13:
Addition on the Cubic / 2.14:
Abel's Theorem / 2.15:
Jacobian Functions: Reprise / 2.16:
Covering Tori / 2.17:
Finale: Higher Genus / 2.18:
Theta Functions / 3.:
Jacobi's Theta Functions / 3.1:
Some Identities / 3.2:
The Jacobi and Weierstrass Connections / 3.3:
Projective Embedding of Tori / 3.4:
Products / 3.5:
Sums of Two Squares / 3.6:
Sums of Four Squares / 3.7:
Euler's Identities: Partitio Numerorum / 3.8:
Jacobi's and Higher Substitutions / 3.9:
Quadratic Reciprocity / 3.10:
Ramanujan's Continued Fractions / 3.11:
Modular Groups and Modular Functions / 4.:
The Modular Group of First Level / 4.1:
The Modular Group of Second Level / 4.2:
Fundamental Cells / 4.3:
Generating the Groups / 4.4:
Gauss on Quadratic Forms / 4.5:
The Group of Anharmonic Ratios / 4.6:
Modular Forms / 4.7:
Eisenstein Sums / 4.8:
Absolute Invariants / 4.9:
Triangle Functions / 4.10:
The Modular Equation of Level 2 / 4.11:
Landen's Transformation / 4.12:
Modular Equations of Higher Level / 4.13:
Jacobi's Modular Equation / 4.14:
Jacobi and Legendre's Derivation: Level 5 / 4.15:
Arithmetic Subgroups: Overview / 4.16:
Ikosaeder and the Quintic / 5.:
Solvability of Equations of Degree [less than] 4 / 5.1:
Galois Groups Revisited / 5.2:
The Galois Group of Level 5 / 5.3:
An Element of Degree 5 / 5.4:
Hermite on the Depressed Equation / 5.5:
Hermite on the Quintic / 5.6:
A Geometric View / 5.7:
Imaginary Quadratic Number Fields / 6.:
Algebraic Numbers / 6.1:
Primes and Ideal Numbers / 6.2:
Class Invariants and Kronecker's Jugendtraum / 6.3:
Application of the Modular Equation / 6.4:
The Class Polynomial / 6.5:
Class Invariants at a Prime Level / 6.6:
Irreducibility of the Class Polynomial / 6.7:
Class Field and Galois Group / 6.8:
Computation of the Class Invariants / 6.9:
Arithmetic of Elliptic Curves / 7:
Arithmetic of the Projective Line / 7.1:
Cubics: The Mordell--Weil Theorem / 7.2:
Proof of the Mordell--Weil Theorem / 7.3:
References
Index
Preface
First Ideas: Complex Manifolds, Riemann Surfaces, and Projective Curves / 1.:
The Riemann Sphere / 1.1:
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