Introduction to modern number theory : fundamental problems, ideas and theories / Yuri Ivanovic Manin, Alexei A. Panchishkin.
""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 inc...
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| Main Authors: | , |
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| Format: | Ebook |
| Language: | English |
| Published: |
Berlin ; New York :
Springer,
[2005]
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| Edition: | Second edition. |
| Series: | Encyclopaedia of mathematical sciences ;
v. 49. |
| Subjects: | |
| Online Access: | Springer eBooks |
| Summary: | ""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)"--Publisher's website. |
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| Item Description: | First ed. originally issued as: Teorii︠a︡ chisel 1, v. 49 of the serial: Itogi i nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalʹnye napravlenii︠a︡. Rev. and updated version of Number theory I. |
| Physical Description: | 1 online resource (xv, 514 pages) : illustrations. |
| Format: | Mode of access: World Wide Web. |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 1280337540 3540276920 9781280337543 9783540276920 |
| ISSN: | 0938-0396 ; |