Number Theory

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Academic Press, 5 мая 1986 г. - Всего страниц: 434
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This book is written for the student in mathematics. Its goal is to give a view of the theory of numbers, of the problems with which this theory deals, and of the methods that are used.

We have avoided that style which gives a systematic development of the apparatus and have used instead a freer style, in which the problems and the methods of solution are closely interwoven. We start from concrete problems in number theory. General theories arise as tools for solving these problems. As a rule, these theories are developed sufficiently far so that the reader can see for himself their strength and beauty, and so that he learns to apply them.

Most of the questions that are examined in this book are connected with the theory of diophantine equations - that is, with the theory of the solutions in integers of equations in several variables. However, we also consider questions of other types; for example, we derive the theorem of Dirichlet on prime numbers in arithmetic progressions and investigate the growth of the number of solutions of congruences.


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Chapter 1 Congruences
Chapter 2 Representation of Numbers by Decomposable Forms
Chapter 3 The Theory of Divisibility
Chapter 4 Local Methods
Chapter 5 Analytic Methods
Algebraic Supplement
Subject Index
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Ссылки на эту книгу

The Arithmetic of Elliptic Curves
Joseph H. Silverman
Недоступно для просмотра - 1986
Algebraic Number Theory
Serge Lang
Ограниченный просмотр - 1994
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Об авторе (1986)

Igor Rostislavovich Shafarevich was born in Zhitomir, Ukraine on June 3, 1923. He graduated from Moscow State University with a specialty in astronomy. He taught at Moscow State University for more than 30 years. He was an internationally renowned mathematician who played a central role in the anti-Soviet dissident movement during the Cold War. His textbooks on algebraic geometry were translated into English and regarded as classics in the field. He also wrote The Socialist Phenomenon and contributed essays to From Under the Rubble. He died on February 19, 2017 at the age of 93.

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