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＜電子ブック＞
Number Theory I : Fundamental Problems, Ideas and Theories / by Yu. I. Manin, Alexei A. Panchishkin
(Encyclopaedia of Mathematical Sciences ; 49)

版	1st ed. 1995.
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
著者標目	*Manin, Yu. I author Panchishkin, Alexei A author SpringerLink (Online service)
件　名	LCSH:Number theory LCSH:Algebraic geometry LCSH:Mathematical logic LCSH:Mathematical physics LCSH:Cryptography LCSH:Data encryption (Computer science) FREE:Number Theory FREE:Algebraic Geometry FREE:Mathematical Logic and Foundations FREE:Mathematical Methods in Physics FREE:Theoretical, Mathematical and Computational Physics FREE:Cryptology
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-662-08005-4

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