Diophantine Approximation on Linear Algebraic Groups - Transcendence Properties of the Exponential Function in Several Variables (Hardcover, 2000 ed.)

The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function ez: a central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. It includes proofs of the main basic results (theorems of Hermite-Lindemann, Gelfond-Schneider, 6 exponentials theorem), an introduction to height functions and Lehmer's problem, several proofs of Baker's theorem as well as explicit measures of linear independence of logarithms. An original feature is the systematic use, in proofs, of Laurent's interpolation determinants. The most general result is the so-called Theorem of the Linear Subgroup, an effective version of which is also included. It yields new results of simultaneous approximation and of algebraic independence. Two chapters written by D. Roy provide complete and at the same time simplified proofs of zero estimates (due to Philippon) on linear algebraic groups.

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Grundlehren der mathematischen Wissenschaften, 326
Release date:	May 2000
First published:	2000
Authors:	Michel Waldschmidt
Dimensions:	235 x 155 x 36mm (L x W x T)
Format:	Hardcover
Pages:	633
Edition:	2000 ed.
ISBN-13:	978-3-540-66785-8
Categories:	Books > Science & Mathematics > Mathematics > Algebra > Groups & group theory Books > Science & Mathematics > Mathematics > Number theory > General
LSN:	3-540-66785-7
Barcode:	9783540667858

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