# Classical Diophantine Equations

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Dezember 1993

## Beschreibung

### Beschreibung

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1982, is mostly superseded.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

### Inhaltsverzeichnis

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.EAN: 9783540573593

ISBN: 3540573593

Untertitel: 'Lecture Notes in Mathematics'.
1993. Auflage.
Book.
Sprache: Englisch.

Verlag: Springer

Erscheinungsdatum: Dezember 1993

Seitenanzahl: 248 Seiten

Format: kartoniert

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