Classical Diophantine Equations / by Vladimir G. Sprindžuk ; edited by Ross Talent.

Format:

Book

Author/Creator:

Sprindzhuk, V. G. (Vladimir Gennadievich), author.

Contributor:

Talent, Ross, editor.

SpringerLink (Online service)

Series:

LOMI and Euler International Mathematical Institute, St.Petersburg ; 1559.

LOMI and Euler International Mathematical Institute, St.Petersburg ; 1559

Language:

English

Subjects (All):

Number theory.

Number Theory.

Local Subjects:

Number Theory.

Physical Description:

1 online resource (XII, 236 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1993.

System Details:

text file PDF

Summary:

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over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded.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.

Contents:

Origins

Algebraic foundations

Linear forms in the logarithms of algebraic numbers

The Thue equation

The Thue-Mahler equation

Elliptic and hyperelliptic equations

Equations of hyperelliptic type

The class number value problem

Reducibility of polynomials and diophantine equations.

Other Format:

Printed edition:

ISBN:

9783540480839

Access Restriction:

Restricted for use by site license.