Introduction to modern number theory : fundamental problems, ideas and theories / Yuri Ivanovic Manin, Alexei A. Panchishkin.

Format:

Book

Author/Creator:

Manin, I︠U︡. I.

Contributor:

Panchishkin, A. A. (Alekseĭ Alekseevich)

Series:

Encyclopaedia of mathematical sciences 0938-0396 ; v. 49.

Encyclopaedia of mathematical sciences, 0938-0396 ; v. 49

Language:

English

Subjects (All):

Number theory.

Physical Description:

xv, 514 pages : illustrations ; 24 cm.

Edition:

Second edition.

Other Title:

Number theory I

Place of Publication:

Berlin ; New York : Springer, [2005]

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.

Notes:

Rev. and updated version of Number theory I, a translation of Teorii͡a chisel 1.

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

ISBN:

3540203648

OCLC:

60785271

Publisher Number:

9783540203643