Introduction to modern number theory
Subtitle: fundamental problems, ideas and theories
By: Yuri Ivanovic Manin, Alexei A. Panchishkin.
Contributors: Panchishkin, A. A.
Edition: 2nd ed., 2nd corr. print.
Series: Encyclopaedia of mathematical sciences -- v. 49
Publisher: Springer
Published: 2007
Place of publication: Berlin; New York
Language: eng
Number of pages: 514
ISBN-13: 9783540203643
Subjects: Number theory.
Other titles: Number theory I
Work titles: Teorii͡a chisel 1.
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)
Notes: A new revised and updated version of "Number theory I. Introduction to number theory" published in 1989 in Moscow, and in English translation of 1995.

Includes bibliographical references (p. [461]-502) and index.