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Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories (Encyclopaedia of Mathematical Sciences)

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Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories (Encyclopaedia of Mathematical Sciences) image
ISBN-10:

3540533842

ISBN-13:

9783540533849

Author(s): Panchishkin, Alexei A.; Manin, Yu.I.
Edition: 1
Released: Nov 10, 1995
Publisher: Springer
Format: Hardcover, 303 pages
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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, the central ideas of modern theories are exposed. The authors have tried to present the most significant results and methods of modern time. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. 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 analysis, representation theory, geometry and algebraic topology.

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