A Panorama of Number Theory or The View from Baker's Garden

A Panorama of Number Theory or The View from Baker's Garden /

This book represents the highlights of a conference hosted at ETH Zurich. It will appeal to a broad spectrum of number theorists. However, it is also for research students interested in the state of number theory at the start of the 21st century and in possible developments for the future.

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Bibliographic Details
Online Access: Full text (MCPHS users only)
Main Author: Wüstholz, Gisbert
Format: Electronic eBook
Language:English
Published: Cambridge : Cambridge University Press, 2002
Series:Cambridge books online.
Subjects:
Number theory > Congresses.
Local Note:ProQuest Ebook Central
Table of Contents:
  • Cover
  • Half-title
  • Title
  • Copyright
  • Contents
  • Contributors
  • Introduction
  • 1 One Century of Logarithmic Forms
  • 1 Introduction
  • 2 Hilbert's seventh problem
  • 3 Elliptic theory
  • 4 Group varieties
  • 5 The quantitative theory
  • 6 The abc-conjecture
  • Bibliography
  • 2 Report on p-adic Logarithmic Forms
  • 1 Historical introduction
  • 2 A successful strategy
  • 3 New developments
  • 4 The application to the abc-conjecture
  • References
  • 3 Recent Progress on Linear Forms in Elliptic Logarithms
  • 1 Introduction
  • 2 New result
  • 3 Key estimate for the refinement.
  • 2.5 Elliptic equations
  • References
  • 5 Baker's Method and Modular Curves
  • Abstract
  • 1 Introduction
  • 2 Heights
  • 3 Baker's method
  • Baker's theorem
  • Functional units
  • Coverings
  • 4 Modular curves
  • Preliminaries
  • Effective Siegel theorem for modular curves
  • Proof of Theorem 10
  • Consequences for elliptic curves
  • References
  • 6 Application of the André-Oort Conjecture to some Questions in Transcendence
  • Abstract
  • 1 Some problems on hypergeometric functions
  • 2 Fuchsian triangle groups
  • 3 Solving Problem 4 solves Problem 1.
  • 4 The André-Oort Conjecture for the Siegel moduli space
  • References
  • 7 Regular Dessins, Endomorphisms of Jacobians, and Transcendence
  • 1 Triangle groups and dessins
  • 2 Integration on regular dessins
  • 3 Shimura families and the Jacobi locus
  • References
  • 8 Maass Cusp Forms with Integer Coefficients
  • Remarks
  • Bibliography
  • 9 Modular Forms, Elliptic Curves and the ABC-Conjecture
  • 1 The ABC-Conjecture
  • 2 Applications of the ABC-Conjecture
  • 3 Elliptic curves over Q (Global Minimal Models)
  • 4 Conjectures which are equivalent to ABC
  • 5 Large Tate-Shafarevich groups.
  • 6 Modular symbols
  • References
  • 10 On the Algebraic Independence of Numbers
  • Abstract
  • 1 E-functions
  • 2 Mahler functions
  • 3 Theorems about functions with addition properties
  • 4 Modular forms
  • 5 Hypergeometric functions
  • 6 Values of theta functions
  • References
  • 11 Ideal Lattices
  • Introduction
  • 1 Definitions, notation and basic facts
  • 2 Integral ideal lattices
  • Quadratic fields
  • Cyclotomic fields of prime power conductor
  • Examples over cyclotomic fields
  • 3 Generalization and examples
  • Knot theory.

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