Complex Analysis in Number Theory

Anatoly A. Karatsuba

CRC Press
Published November 22, 1994
Reference - 208 Pages
ISBN 9780849328664 - CAT# 2866


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  • Presents a survey of the application of complex analysis in the theory of prime numbers
  • Offers an easy-to-understand presentation of the theory of distribution of prime numbers
  • Provides full proof of state-of-the-art results in the Riemann theory of zeta-function
  • Discusses philosophic aspects of universal properties of Riemann's zeta-function and the structure of the Universe
  • Contains several arithmetic problems dealing with number theory
  • Summary

    This book examines the application of complex analysis methods to the theory of prime numbers. In an easy to understand manner, a connection is established between arithmetic problems and those of zero distribution for special functions. Main achievements in this field of mathematics are described. Indicated is a connection between the famous Riemann zeta-function and the structure of the universe, information theory, and quantum mechanics. The theory of Riemann zeta-function and, specifically, distribution of its zeros are presented in a concise and comprehensive way. The full proofs of some modern theorems are given. Significant methods of the analysis are also demonstrated as applied to fundamental problems of number theory.