A panorama in number theory or the view from Baker's garden

목차 (Table of Contents)

• CONTENTS
• Contributors = ⅶ
• Introduction = xi
• 1 One Century of Logarithmic Forms / G. W$$\ddot u$$stholz = 1
• 2 Report on p-adic Logarithmic Forms / Kunrui Yu = 11
• 3 Recent Progress on Linear Forms in Elliptic Logarithms / Sinnou David ; Noriko Hirata-Kohno = 26
• 4 Solving Diophantine Equations by Baker's Theory / K$$\acute a$$lm$$\acute a$$n Gy$$\H{o}$$ry = 38
• 5 Baker's Method and Modular Curves / Yuri F. Bilu = 73
• 6 Application of the Andr$$\acute e$$-Oort Conjecture to some Questions in Transcendence / Paula B. Cohen ; Gisbert W$$\ddot u$$stholz = 89
• 7 Regular Dessins, Endomorphisms of Jacobians, and Transcendence / J$$\ddot u$$rgen Wolfart = 107
• 8 Maass Cusp Forms with Integer Coefficients / Peter Sarnak = 121
• 9 Modular Forms, Elliptic Curves and the ABC-Conjecture / Dorian Goldfeld = 128
• 10 On the Algebraic Independence of Numbers / Yu.V.Nesterenko = 148
• 11 Ideal Lattices / Eva Bayer-Fluckiger = 168
• 12 Integral Points and Mordell-Weil Lattices / Tetsuji Shioda = 185
• 13 Forty Years of Effective Results in Diophantine Theory / Enrico Bombieri = 194
• 14 Points on Subvarieties of Tori / Jan-Hendrik Evertse = 214
• 15 A New Application of Diophantine Approximations / G. Faltings = 231
• 16 Search Bounds for Diophantine Equations / D.W. Masser = 247
• 17 Regular Systems, Ubiquity and Diophantine Approximation / V.V. Beresnevich ; V.I. Bernik ; M.M. Dodson = 260
• 18 Diophantine Approximation, Lattices and Flows on Homogeneous Spaces / Gregory Margulis = 280
• 19 On Linear Ternary Equations with Prime Variables - Baker's Constant and Vinogradov's Bound / Ming-Chit Liu ; Tianze Wang = 311
• 20 Powers in Arithmetic progression / T.N. Shorey = 325
• 21 On the Greatest Common Divisor of Two Univariate Polynomials, Ⅰ / A. Schinzel = 337
• 22 Heilbronn's Exponential Sum and Transcendence Theory / D.R. Heath-Brown = 353