Introduction to Modern Number Theory
(Sprache: Englisch)
This edition has been called 'startlingly up-to-date', and in this corrected second printing you can be sure that it's even more contemporaneous. It surveys from a unified point of view both the modern state and the trends of continuing development in...
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This edition has been called 'startlingly up-to-date', and in this corrected second printing you can be sure that it's even more contemporaneous. It surveys from a unified point of view both the modern state and the trends of continuing development in various branches of number theory. Illuminated by elementary problems, the central ideas of modern theories are laid bare. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories.
Klappentext zu „Introduction to Modern Number Theory “
This edition has been called 'startlingly up-to-date', and in this corrected second printing you can be sure that it's even more contemporaneous. It surveys from a unified point of view both the modern state and the trends of continuing development in various branches of number theory. Illuminated by elementary problems, the central ideas of modern theories are laid bare. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories.
Introduction to Modern Number Theory surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems, the central ideas of modern theories are exposed. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions.
This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories. Moreover, the authors have added a part dedicated to arithmetical cohomology and noncommutative geometry, a report on point counts on varieties with many rational points, the recent polynomial time algorithm for primality testing, and some others subjects.
From the reviews of the 2nd edition:
"... For my part, I come to praise this fine volume. This book is a highly instructive read ... the quality, knowledge, and expertise of the authors shines through. ... The present volume is almost startlingly up-to-date ..." (A. van der Poorten, Gazette, Australian Math. Soc. 34 (1), 2007)
This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories. Moreover, the authors have added a part dedicated to arithmetical cohomology and noncommutative geometry, a report on point counts on varieties with many rational points, the recent polynomial time algorithm for primality testing, and some others subjects.
From the reviews of the 2nd edition:
"... For my part, I come to praise this fine volume. This book is a highly instructive read ... the quality, knowledge, and expertise of the authors shines through. ... The present volume is almost startlingly up-to-date ..." (A. van der Poorten, Gazette, Australian Math. Soc. 34 (1), 2007)
Inhaltsverzeichnis zu „Introduction to Modern Number Theory “
- Problems and Tricks- Number Theory
- Some Applications of Elementary Number Theory
- Ideas and Theories
- Induction and Recursion
- Arithmetic of algebraic numbers
- Arithmetic of algebraic varieties
- Zeta Functions and Modular Forms
- Fermat's Last Theorem and Families of Modular Forms
- Analogies and Visions
- Introductory survey to part III: motivations and description
- Arakelov Geometry and Noncommutative Geometry (d'après C. Consani and M. Marcolli, [CM])
Bibliographische Angaben
- Autoren: Yu. I. Manin , Alexei A. Panchishkin
- 2005, 2. A., 514 Seiten, Maße: 16,7 x 24,2 cm, Gebunden, Englisch
- Herausgegeben: A. N. Parshin, I. R. Shafarevich
- Übersetzer: Yuri Ivanovich Manin, A. A. Panchishkin
- Verlag: Springer
- ISBN-10: 3540203648
- ISBN-13: 9783540203643
Sprache:
Englisch
Rezension zu „Introduction to Modern Number Theory “
"Das vorliegende Buch gibt einen sehr konzisen Blick auf die Zahlentheorie, beginnend mit den historischen Anfängen bis hin zu neuesten Resultaten und Sichtweisen. Daß bei einem solch weit gespannten Themenkreis nicht immer der Charaketer einer "Einführung" gewahrt werden kann, ist klar. ... Nichtsdestotrotz ist es den Autoren gelungen, eine beeindruckende Gesamtschau der Zahlentheorie bis hin zu den Entwicklungen der letzten Jahre zu geben. ... "P.Grabner, Internationale Mathematische Nachrichten 201, p. 37-38, 2006
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