Number Theory I : Fundamental Problems, Ideas and Theories / edited by A. N. Parshin, I. R. Shafarevich
(Encyclopaedia of Mathematical Sciences ; 49)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
| 出版年 | 1995 |
| 本文言語 | 英語 |
| 大きさ | V, 306 p : online resource |
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| 内容注記 | I. Problems and Tricks 1. Elementary Number Theory 2. Some Modern Problems of Elementary Number Theory II. Ideas and Theories 1. Induction and Recursion 2. Arithmetic of Algebraic Numbers 3. Arithmetic of Algebraic Varieties 4. Zeta Functions and Modular Forms References |
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| 一般注記 | This book 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 (including some modern areas such as cryptography, factorization and primality testing), the central ideas of modern theories are exposed: algebraic number theory, calculations and properties of Galois groups, non-Abelian generalizations of class field theory, recursive computability and links with Diophantine equations, the arithmetic of algebraic varieties, connections with modular forms, zeta- and L-functions. The authors have tried to present the most significant results and methods of modern time. An overview of the major conjectures is also given in order to illustrate current thinking in number theory. Most of these conjectures are based on analogies between functions and numbers, and on connections with other branches of mathematics such as algebraic topology, analysis, representation theory and geometry |
| 著者標目 | Parshin, A. N. editor Shafarevich, I. R. editor SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Data encryption (Computer science) LCSH:Algebraic geometry LCSH:Mathematical logic LCSH:Number theory LCSH:Physics FREE:Mathematics FREE:Number Theory FREE:Algebraic Geometry FREE:Mathematical Logic and Foundations FREE:Mathematical Methods in Physics FREE:Numerical and Computational Physics FREE:Data Encryption |
| 分 類 | DC23:512.7 |
| 巻冊次 | ISBN:9783662080054 
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| ISBN | 9783662080054 |
| URL | http://dx.doi.org/10.1007/978-3-662-08005-4 |
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