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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Содержание

Chapter 1 Congruences
1
Chapter 2 Representation of Numbers by Decomposable Forms
75
Chapter 3 The Theory of Divisibility
155
Chapter 4 Local Methods
251
Chapter 5 Analytic Methods
309
Algebraic Supplement
390
Tables
422
Subject Index
433
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The Arithmetic of Elliptic Curves
Joseph H. Silverman
Недоступно для просмотра - 1986
Algebraic Number Theory
Serge Lang
Ограниченный просмотр - 1994
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