Overview

""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)

Full Product Details

9783642057977

Table of Contents

Reviews

Das vorliegende Buch gibt einen sehr konzisen Blick auf die Zahlentheorie, beginnend mit den historischen Anfangen bis hin zu neuesten Resultaten und Sichtweisen. Dass bei einem solch weit gespannten Themenkreis nicht immer der Charaketer einer Einfuhrung 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

Author Information

Tab Content 6

Customer Reviews

Recent Reviews

Countries Available