reine Buchbestellungen ab 5 Euro senden wir Ihnen Portofrei zuDiesen Artikel senden wir Ihnen ohne weiteren Aufpreis als PAKET

Number Theory IV
(Englisch)
Transcendental Numbers
Parshin, A. N. & Shafarevich, I. R. & Fel\'dman, N. I. & Nesterenko, Yu.V.

Print on Demand - Dieser Artikel wird für Sie gedruckt!

127,45 €

inkl. MwSt. · Portofrei
Dieses Produkt wird für Sie gedruckt, Lieferzeit ca. 14 Werktage
Menge:

Number Theory IV

Seiten
Erscheinungsdatum
Auflage
Ausstattung
Erscheinungsjahr
Sprache
Abbildungen
Serienfolge
Erscheinungsland
alternative Ausgabe
Vertrieb
Kategorie
Buchtyp
Warengruppenindex
Warengruppe
Detailwarengruppe
Uebersetzer
Features
Laenge
Breite
Hoehe
Gewicht
Herkunft
Relevanz
Referenznummer
Moluna-Artikelnummer

Produktbeschreibung

This book is a survey of the most important directions of research in transcendental number theory. For readers with no specific background in transcendental number theory, the book provides both an overview of the basic concepts and techniques and also a guide to the most important results and references.

|This book was written over a period of more than six years. Several months after we finished our work, N.1. Fel'dman (the senior author of the book) died. All additions and corrections entered after his death were made by his coauthor. The assistance of many of our colleagues was invaluable during the writing of the book. They examined parts of the manuillegalscript and suggested many improvements, made useful comments and corrected many errors. I much have pleasure in acknowledging our great indebtedness to them. Special thanks are due to A. B. Shidlovskii, V. G. Chirskii, A.1. Galochkin and O. N. Vasilenko. I would like to express my gratitude to D. Bertrand and J. Wolfart for their help in the final stages of this book. Finally, I wish to thank Neal Koblitz for having translated this text into English. August 1997 Yu. V.Nesterenko Transcendental Numbers N.1. Fel'dman and Yu. V. Nesterenko Translated from the Russian by Neal Koblitz Contents Notation ...................................................... 9 Introduction ................................................... 11 0.1 Preliminary Remarks .................................. 11 0.2 Irrationality of J2 ..................................... 11 0.3 The Number 1C' ---------------------------------------- 13 0.4 Transcendental Numbers ............................... 14 0.5 Approximation of Algebraic Numbers .................... 15 0.6 Transcendence Questions and Other Branches of Number Theory ..................................... 16 0.7 The Basic Problems Studied in Transcendental Number Theory ....................................... 17 0.8 Different Ways of Giving the Numbers ................... 19 0.9 Methods .......................... . . . . . . . . . . . . . . 20 . . . . .|The book treats an important special subject in number theory. It is appropriate for graduate students and researchers in number theory and other mathematicians who are looking for a reference on transcendental number theory.
1. Approximation of Algebraic Numbers.- 2. Effective Constructions in Transcendental Number Theory.- 3. Hilbert´s Seventh Problem.- 4. Multidimensional Generalization of Hilbert´s Seventh Problem.- 5. Values of Analytic Functions That Satisfy Linear Differential Equations.- 6. Algebraic Independence of the Values of Analytic Functions That Have an Addition Law.
This book is a survey of the most important directions of research in transcendental number theory. The central topics in this theory include proofs of irrationality and transcendence of various numbers, especially those that arise as the values of special functions. Questions of this sort go back to ancient times. An example is the old problem of squaring the circle, which Lindemann showed to be impossible in 1882, when he proved that $Öpi$ is a transcendental number. Euler's conjecture that the logarithm of an algebraic number to an algebraic base is transcendental was included in Hilbert's famous list of open problems; this conjecture was proved by Gel'fond and Schneider in 1934. A more recent result was ApÖ'ery's surprising proof of the irrationality of $Özeta(3)$ in 1979. The quantitative aspects of the theory have important applications to the study of Diophantine equations and other areas of number theory. For a reader interested in different branches of number theory, this monograph provides both an overview of the central ideas and techniques of transcendental number theory, and also a guide to the most important results.


1. Approximation of Algebraic Numbers.- 2. Effective Constructions in Transcendental Number Theory.- 3. Hilbert's Seventh Problem.- 4. Multidimensional Generalization of Hilbert's Seventh Problem.- 5. Values of Analytic Functions That Satisfy Linear Differential Equations.- 6. Algebraic Independence of the Values of Analytic Functions That Have an Addition Law.


Inhaltsverzeichnis



1. Approximation of Algebraic Numbers.- 2. Effective Constructions in Transcendental Number Theory.- 3. Hilbert¿s Seventh Problem.- 4. Multidimensional Generalization of Hilbert¿s Seventh Problem.- 5. Values of Analytic Functions That Satisfy Linear Differential Equations.- 6. Algebraic Independence of the Values of Analytic Functions That Have an Addition Law.


Klappentext



This book is a survey of the most important directions of research in transcendental number theory. For readers with no specific background in transcendental number theory, the book provides both an overview of the basic concepts and techniques and also a guide to the most important results and references.




The book treats an important special subject in number theory. It is appropriate for graduate students and researchers in number theory and other mathematicians who are looking for a reference on transcendental number theory.



Datenschutz-Einstellungen