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1.

図書
図書
1. Modular forms and Fermat's last theorem
Gary Cornell, Joseph H. Silverman, Glenn Stevens, editors
出版情報: New York : Springer, c1997  xix, 582 p. ; 25 cm
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2.

図書
図書
2. Advanced topics in the arithmetic of elliptic curves (: us : hard - : gw : soft)
Joseph H. Silverman
出版情報: New York ; Tokyo : Springer-Verlag, c1994  xiii, 525 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 151
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Preface
Introduction
Elliptic and Modular Functions
Complex Multiplication
Elliptic Surfaces
The NFron Model
Elliptic Curves over Complete Fields
Local Height Functions
Some Useful Tables / Appendix A：
Notes on Exercises
References
List of Notation
Index
Preface
Introduction
Elliptic and Modular Functions
3.

図書
図書
3. Cryptography and lattices : International Conference, CaLC 2001, Providence, RI, USA, March 29-30, 2001 : revised papers
Joseph H. Silverman (ed.)
出版情報: Berlin ; Tokyo : Springer, c2001  vi, 217 p. ; 24 cm
シリーズ名: Lecture notes in computer science ; 2146
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4.

図書
図書
4. Advanced topics in the arithmetic of elliptic curves. 2nd corr. printing (: us : hard - : gw : soft)
Joseph H. Silverman
出版情報: New York ; Tokyo : Springer-Verlag, 1999, c1994  xiii, 525 p. ; 24 cm
シリーズ名: Graduate texts in mathematics ; 151
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目次情報: 続きを見る
Preface
Introduction
Elliptic and Modular Functions
Complex Multiplication
Elliptic Surfaces
The NFron Model
Elliptic Curves over Complete Fields
Local Height Functions
Some Useful Tables / Appendix A：
Notes on Exercises
References
List of Notation
Index
Preface
Introduction
Elliptic and Modular Functions
5.

図書
図書
5. Moduli spaces and arithmetic dynamics
Joseph H. Silverman
出版情報: Providence, R.I. : American Mathematical Society, c2012  vii, 140 p. ; 26 cm
シリーズ名: CRM monograph series ; v. 30
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6.

図書
図書
6. Arithmetic geometry (: us ; : gw ; : [softcover])
edited by Gary Cornell, Joseph H. Silverman ; with contributions by M. Artin ... [et al.]
出版情報: New York ; Tokyo : Springer-Verlag, c1986  xiv, 353 p. ; 25 cm
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7.

図書
図書
7. The arithmetic of elliptic curves (: us ; : gw)
Joseph H. Silverman
出版情報: New York ; Berlin ; Tokyo : Springer-Verlag, c1986  xii, 400 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 106
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Algebraic Varieties
The Geometry of Elliptic Curves
The Formal Group of an Elliptic Curve
Elliptic Curves over Finite Fields
Elliptic Curves over C
Elliptic Curves over Local Fields
Elliptic Curves over Global Fields
Integral Points on Elliptic Curves
Computing the Mordell-Weil Group
Appendices
Algebraic Varieties
The Geometry of Elliptic Curves
The Formal Group of an Elliptic Curve
8.

図書
図書
8. A friendly introduction to number theory. 2nd ed
Joseph H. Silverman
出版情報: Upper Saddle River, NJ : Prentice Hall, c2001  vii, 386 p. ; 24 cm
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Preface
Introduction
What Is Number Theory? / Chapter 1.：
Pythagorean Triples / Chapter 2.：
Pythagorean Triples and the Unit Circle / Chapter 3.：
Sums of Higher Powers and Fermat's Last Theorem / Chapter 4.：
Divisibility and the Greatest Common Divisor / Chapter 5.：
Linear Equations and the Greatest Common Divisor / Chapter 6.：
Factorization and the Fundamental Theorem of Arithmetic / Chapter 7.：
Congruences / Chapter 8.：
Congruences, Powers, and Fermat's Little Theorem / Chapter 9.：
Congruences, Powers, and Euler's Formula / Chapter 10.：
Euler's Phi Function / Chapter 11.：
Prime Numbers / Chapter 12.：
Counting Primes / Chapter 13.：
Mersenne Primes / Chapter 14.：
Mersenne Primes and Perfect Numbers / Chapter 15.：
Powers Modulo m and Successive Squaring / Chapter 16.：
Computing k[superscript th] Roots Modulo m / Chapter 17.：
Powers, Roots, and "Unbreakable" Codes / Chapter 18.：
Euler's Phi Function and Sums of Divisors / Chapter 19.：
Powers Modulo p and Primitive Roots / Chapter 20.：
Primitive Roots and Indices / Chapter 21.：
Squares Modulo p / Chapter 22.：
Is - 1 a Square Modulo p? Is 2? / Chapter 23.：
Quadratic Reciprocity / Chapter 24.：
Which Primes Are Sums of Two Squares? / Chapter 25.：
Which Numbers Are Sums of Two Squares? / Chapter 26.：
The Equation X[superscript 4] + Y[superscript 4] = Z[superscript 4] / Chapter 27.：
Square-Triangular Numbers Revisited / Chapter 28.：
Pell's Equation / Chapter 29.：
Diophantine Approximation / Chapter 30.：
Diophantine Approximation and Pell's Equation / Chapter 31.：
Primality Testing and Carmichael Numbers / Chapter 32.：
Number Theory and Imaginary Numbers / Chapter 33.：
The Gaussian Integers and Unique Factorization / Chapter 34.：
Irrational Numbers and Transcendental Numbers / Chapter 35.：
Binomial Coefficients and Pascal's Triangle / Chapter 36.：
Fibonacci's Rabbits and Linear Recurrence Sequences / Chapter 37.：
Generating Functions / Chapter 38.：
Sums of Powers / Chapter 39.：
Cubic Curves and Elliptic Curves / Chapter 40.：
Elliptic Curves with Few Rational Points / Chapter 41.：
Points on Elliptic Curves Modulo p / Chapter 42.：
Torsion Collections Modulo p and Bad Primes / Chapter 43.：
Defect Bounds and Modularity Patterns / Chapter 44.：
Elliptic Curves and Fermat's Last Theorem / Chapter 45.：
Further Reading
Factorization of Small Composite Integers / Appendix A.：
A List of Primes / Appendix B.：
Index
Preface
Introduction
What Is Number Theory? / Chapter 1.：
9.

図書
図書
9. Diophantine geometry : an introduction (: hbk ; : pbk)
Marc Hindry, Joseph H. Silverman
出版情報: New York : Springer-Verlag, c2000  xiii, 558 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 201
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Preface
Acknowledgments
Contents
Detailed Contents for Part A
Introduction
The Geometry of Curves and Abelian Varieties / Part A：
Algebraic Varieties / A.1：
Divisors / A.2：
Linear Systems / A.3：
Algebraic Curves / A.4：
Abelian Varieties over C / A.5：
Jacobians over C / A.6：
Abelian Varieties over Arbitrary Fields / A.7：
Jacobians over Arbitrary Fields / A.8：
Schemes / A.9：
Height Functions / Part B：
Absolute Values / B.1：
Heights on Projective Space / B.2：
Heights on Varieties / B.3：
Canonical Height Functions / B.4：
Canonical Heights on Abelian Varieties / B.5：
Counting Rational Points on Varieties / B.6：
Heights and Polynomials / B.7：
Local Height Functions / B.8：
Canonical Local Heights on Abelian Varieties / B.9：
Introduction to Arakelov Theory / B.10：
Exercises
Rational Points on Abelian Varieties / Part C：
The Weak Mordell-Weil Theorem / C.1：
The Kernel of Reduction Modulo p / C.2：
Finiteness Theorems in Algebraic Number Theory / C.3 Appendix：
The Selmer and Tate-Shafarevich Groups / C.4 Appendix：
Galois Cohomology and Homogeneous Spaces / C.5 Appendix：
Diophantine Approximation and Integral Points on Curves / Part D：
Two Elementary Results on Diophantine Approximation / D.1：
Roth's Theorem / D.2：
Preliminary Results / D.3：
Construction of the Auxiliary Polynomial / D.4：
The Index Is Large / D.5：
The Index Is Small (Roth's Lemma) / D.6：
Completion of the Proof of Roth's Theorem / D.7：
Application: The Unit Equation U + V = 1 / D.8：
Application: Integer Points on Curves / D.9：
Rational Points on Curves of Genus at Least 2 / Part E：
Vojta's Geometric Inequality and Faltings' Theorem / E.1：
Pinning Down Some Height Functions / E.2：
An Outline of the Proof of Vojta's Inequality / E.3：
An Upper Bound for h[subscript Omega](z, w) / E.4：
A Lower Bound for h[subscript Omega](z, w) for Nonvanishing Sections / E.5：
Constructing Sections of Small Height I: Applying Riemann-Roch / E.6：
Constructing Sections of Small Height II: Applying Siegel's Lemma / E.7：
Lower Bound for h[subscript Omega](z, w) at Admissible (i*[subscript 1], i*[subscript 2]): Version I / E.8：
Eisenstein's Estimate for the Derivatives of an Algebraic Function / E.9：
Lower Bound for h[subscript Omega](z, w) at Admissible (i*[subscript 1], i*[subscript 2]): Version II / E.10：
A Nonvanishing Derivative of Small Order / E.11：
Completion of the Proof of Vojta's Inequality / E.12：
Further Results and Open Problems / Part F：
Curves and Abelian Varieties / F.1：
Rational Points on Subvarieties of Abelian Varieties / F.1.1：
Application to Points of Bounded Degree on Curves / F.1.2：
Discreteness of Algebraic Points / F.2：
Bogomolov's Conjecture / F.2.1：
The Height of a Variety / F.2.2：
Height Bounds and Height Conjectures / F.3：
The Search for Effectivity / F.4：
Effective Computation of the Mordell-Weil Group A([kappa]) / F.4.1：
Effective Computation of Rational Points on Curves / F.4.2：
Quantitative Bounds for Rational Points / F.4.3：
Geometry Governs Arithmetic / F.5：
Kodaira Dimension / F.5.1：
The Bombieri-Lang Conjecture / F.5.2：
Vojta's Conjecture / F.5.3：
Varieties Whose Rational Points Are Dense / F.5.4：
References
List of Notation
Index
Affine and Projective Varieties / A.1.1：
Algebraic Maps and Local Rings / A.1.2：
Dimension / A.1.3：
Tangent Spaces and Differentials / A.1.4：
Weil Divisors / A.2.1：
Cartier Divisors / A.2.2：
Intersection Numbers / A.2.3：
Linear Systems and Maps / A.3.1：
Ampleness and the Enriques-Severi-Zariski Lemma / A.3.2：
Line Bundles and Sheaves / A.3.3：
Birational Models of Curves / A.4.1：
Genus of a Curve and the Riemann-Roch Theorem / A.4.2：
Curves of Genus 0 / A.4.3：
Curves of Genus 1 / A.4.4：
Curves of Genus at Least 2 / A.4.5：
Algebraic Surfaces / A.4.6：
Complex Tori / A.5.1：
Divisors, Theta Functions, and Riemann Forms / A.5.2：
Riemann-Roch for Abelian Varieties / A.5.3：
Abelian Integrals / A.6.1：
Periods of Riemann Surfaces / A.6.2：
The Jacobian of a Riemann Surface / A.6.3：
Albanese Varieties / A.6.4：
Generalities / A.7.1：
Divisors and the Theorem of the Cube / A.7.2：
Dual Abelian Varieties and Poincare Divisors / A.7.3：
Construction and Properties / A.8.1：
The Divisor [Theta] / A.8.2：
Families of Subvarieties / A.8.3 Appendix：
Varieties over Z / A.9.1：
Analogies Between Number Fields and Function Fields / A.9.2：
Minimal Model of a Curve / A.9.3：
Neron Model of an Abelian Variety / A.9.4：
Preface
Acknowledgments
Contents
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