Ebook: Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories

"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)

With the second edition widely praised for its authoritative yet approachable style, in this corrected second printing you can be sure this excellent work is even more contemporaneous.

It surveys from a unified point of view both the modern state and the trends of continuing development in various branches of number theory.

Illuminated by elementary problems, the central ideas of modern theories are laid bare. 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.

What’s more, the authors have added a segment dedicated to arithmetical cohomology and noncommutative geometry as well as a report on point counts on varieties with many rational points.

Also covered is the recent polynomial time algorithm for primality testing, among other subjects.

From the reviews of the 2nd edition: "… For my part, I come to praise this fine volu

With the second edition widely praised for its authoritative yet approachable style, in this corrected second printing you can be sure this excellent work is even more contemporaneous.

It surveys from a unified point of view both the modern state and the trends of continuing development in various branches of number theory.

Illuminated by elementary problems, the central ideas of modern theories are laid bare. 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.

What’s more, the authors have added a segment dedicated to arithmetical cohomology and noncommutative geometry as well as a report on point counts on varieties with many rational points.

Also covered is the recent polynomial time algorithm for primality testing, among other subjects.

From the reviews of the 2nd edition: "… For my part, I come to praise this fine volu
Content:
Front Matter....Pages I-6
Front Matter....Pages 7-7
Number Theory....Pages 9-61
Some Applications of Elementary Number Theory....Pages 63-91
Front Matter....Pages 93-93
Induction and Recursion....Pages 95-114
Arithmetic of algebraic numbers....Pages 115-189
Arithmetic of algebraic varieties....Pages 191-259
Zeta Functions and Modular Forms....Pages 261-340
Fermat’s Last Theorem and Families of Modular Forms....Pages 341-393
Front Matter....Pages 395-395
Introductory survey to part III: motivations and description....Pages 397-413
Arakelov Geometry and Noncommutative Geometry (d’apr?s C. Consani and M. Marcolli, [CM])....Pages 415-460
Arakelov Geometry and Noncommutative Geometry (d’apr?s C. Consani and M. Marcolli, [CM])....Pages 415-460
Back Matter....Pages 461-514

With the second edition widely praised for its authoritative yet approachable style, in this corrected second printing you can be sure this excellent work is even more contemporaneous.

It surveys from a unified point of view both the modern state and the trends of continuing development in various branches of number theory.

Illuminated by elementary problems, the central ideas of modern theories are laid bare. 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.

What’s more, the authors have added a segment dedicated to arithmetical cohomology and noncommutative geometry as well as a report on point counts on varieties with many rational points.

Also covered is the recent polynomial time algorithm for primality testing, among other subjects.

From the reviews of the 2nd edition: "… For my part, I come to praise this fine volu
Content:
Front Matter....Pages I-6
Front Matter....Pages 7-7
Number Theory....Pages 9-61
Some Applications of Elementary Number Theory....Pages 63-91
Front Matter....Pages 93-93
Induction and Recursion....Pages 95-114
Arithmetic of algebraic numbers....Pages 115-189
Arithmetic of algebraic varieties....Pages 191-259
Zeta Functions and Modular Forms....Pages 261-340
Fermat’s Last Theorem and Families of Modular Forms....Pages 341-393
Front Matter....Pages 395-395
Introductory survey to part III: motivations and description....Pages 397-413
Arakelov Geometry and Noncommutative Geometry (d’apr?s C. Consani and M. Marcolli, [CM])....Pages 415-460
Arakelov Geometry and Noncommutative Geometry (d’apr?s C. Consani and M. Marcolli, [CM])....Pages 415-460
Back Matter....Pages 461-514
....