CLASSICAL DIOPHANTINE EQUATIONS by Vladimir G. Sprindzuk ( 9783540573593 )

Item Details

Title:

CLASSICAL DIOPHANTINE EQUATIONS

By:

Format:

Paperback

List price:	£40.99
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ISBN 10:

3540573593

ISBN 13:

9783540573593

Publisher:

SPRINGER-VERLAG BERLIN AND HEIDELBERG GMBH & CO. KG

Pub. date:

20 December, 1993

Series:

Lecture Notes in Mathematics / Lomi and Euler International Mathematical v. 1559

Pages:

236

Description:

This monograph provides a detailed discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to the obtaining of upper bounds for solutions to the eponymous classical diophantine equation.

Synopsis:

The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, now that the book appears in English, close studyand emulation.In particular those emphases allow him to devote the eighth chapter to an analysis of the interrelationship of the class number of algebraic number fields involved and the bounds on the heights of thesolutions of the diophantine equations. Those ideas warrant further development. The final chapter deals with effective aspects of the Hilbert Irreducibility Theorem, harkening back to earlier work of the author. There is no other congenial entry point to the ideas of the last two chapters in the literature.

Illustrations:

biography

Publication:

Germany

Imprint:

Springer-Verlag Berlin and Heidelberg GmbH & Co. K

Returns:

Returnable

Some other items by this author:

METRIC THEORY OF DIOPHANTINE APPROXIMATIONS (HB)