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Diophantine Approximation on Linear Algebraic Groups

Name: Diophantine Approximation on Linear Algebraic Groups
Brand: Springer, Berlin
SKU: 9783642086083
Price: 423.12 PLN
Availability: InStock

Transcendence Properties of the Exponential Function in Several Variables

Autor: Michel Waldschmidt

Język:

Oprawa: Miękka

Wydawca: Springer, Berlin

Dostępność: Dostępna u dostawcy

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The theory of transcendental numbers is closely related to the study of diophantine approximation. T...

Informacje o książce

Autor

Michel Waldschmidt

Język

Angielski

Oprawa

Książka - Miękka

Data wydania

2010

strony

633

EAN

9783642086083

ISBN

364208608X

Enbook ID

05281131

Wydawca

Springer, Berlin

Waga

917

Wymiary

155 x 235 x 33

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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 ez: a central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. Two chapters provide complete and simplified proofs of zero estimates (due to Philippon) on linear algebraic groups. 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 the main basic results (theorems of Hermite-Lindemann, Gelfond-Schneider, 6 exponentials theorem), an introduction to height functions with a discussion of Lehmer's problem, several proofs of Baker's theorem as well as explicit measures of linear independence of logarithms. An original feature is that proofs make systematic use 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. 2 chapters written by D. Roy provide complete and at the same time simplified proofs of zero estimates (due to P. Philippon) on linear algebraic groups.

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Diophantine Approximation on Linear Algebraic Groups

Transcendence Properties of the Exponential Function in Several Variables

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