Number Theory I
Subtitle: Fundamental Problems, Ideas and Theories
By: edited by A. N. Parshin, I. R. Shafarevich
Contributors: Shafarevich, I. R.
Series: Encyclopaedia of Mathematical Sciences -- 49; Encyclopaedia of Mathematical Sciences -- 49
Publisher: Springer Berlin Heidelberg
Published: 1995
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] :
Number of pages: 306
ISBN-13: 9783662080078; 9783662080054
Subjects: Mathematical physics; Symbolic and mathematical Logic; Data encryption (Computer science); Mathematics; Geometry, algebraic; Number theory
Description: 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.
Notes: Online full text is restricted to subscribers.

Also available in print.

Mode of access: World Wide Web.