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.
- ISBN10 3540800395
- ISBN13 9783540800392
- Publish Date 4 September 2008 (first published September 1995)
- Publish Status Withdrawn
- Out of Print 18 October 2014
- Publish Country US
- Imprint Springer
- Format Paperback (US Trade)
- Pages 532
- Language English