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Diophantine Approximation on Linear Algebraic Groups : Transcendence Properties of the Exponential Function in Several Variables /

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The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function e^z. A central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. This book includes proofs of th...

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Bibliographic Details
Main Author: Waldschmidt, Michel
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2000.
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics ; 326.
Subjects:
Mathematics.
Geometry, Algebraic.
Group theory.
Number theory.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Introduction and Historical Survey
  • Part I. Linear Independence of Logarithms of Algebraic Numbers. Transcendence Proofs in One Variable. Heights of Algebraic Numbers. The Criterion of Schneider-Lang. Zero Estimate. Linear Independence of Logarithms of Algebraic Numbers
  • Part II. Measures of Linear Independence. A First Measure with a Simple Proof. Zero Estimate (Continued), by Damien ROY. Refined Measure
  • Part III. Multiplicities in Higher Dimension Multiplicity Estimates, by Damien ROY. Interpolation Determinants with One Derivative. On Baker's Method
  • Part IV. The Linear Subgroup Theorem. Points Whose Coordinates are Logarithms of Algebraic Numbers. Lower Bounds for the Rank of Matrices
  • Part V. Simultaneous Approximation of Values of the Exponential Function in Several Variables. A Quantitative Version of the Linear Subgroup Theorem. Applications to Diophantine Approximation. Algebraic Independence
  • References.