ENGLISH

Introduction to modern number theory fundamental problems ideas and theories

By Yu. I. Manin , Alexei A. Panchishkin

Book information

Publisher
Springer
Year
2007
ISBN
9783540203643, 3-540-20364-8, 3540203648
LCC
QA241 .T2713 2007
Open Library ID
OL18263647M
Language
english
Format
PDF
Filesize
2 MB (2612644 bytes)
Series
Encyclopaedia of Mathematical Sciences 49
Edition
2nd
Pages
520\520
Library
Springer
Time added
2009-08-06 07:02:15

Description

"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)

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