Overview

Intended for mathematicians, this book surveys applications of complex analysis methods to the theory of prime numbers. A connection is made between arithmetic problems and those of zero distribution for special functions. The main achievements in this field of mathematics are described, and a connection between the Riemann zeta-function and problems of cosmology, information theory and quantum mechanics is indicated.

Full Product Details

Author:   Anatoly A. Karatsuba (Steklov Mathematical Institute, Moscow, Russia)
Publisher:   Taylor & Francis Inc
Imprint:   CRC Press Inc
Dimensions:   Width: 15.60cm , Height: 1.70cm , Length: 23.40cm
Weight:   0.476kg
ISBN:  

9780849328664

ISBN 10:   0849328667
Pages:   208
Publication Date:   22 November 1994
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

The Complex Integration Method and Its Application in Number Theory Generating Functions in Number Theory Summation Formula Riemann's Zeta-Function and Its Simplest Properties The Theory of Riemann's Zeta-Function Zeros on the Critical Line The Boundary of Zeros Approximate Equations of the z(s) Function The Method of Trigonometric Sums in the Theory of the z(s) Function Density Theorems The Order of Growth of |z(s)| in a Critical Strip Universal Properties of the z(s) Function Riemann's Hypothesis, Its Equivalents, Computations Dirichlet L-Functions: Dirichlet's Characters Dirichlet L-Functions and Prime Numbers in Arithmetic Progressions Zeros of L-Functions Real Zeros of L-Functions and the Number of Classes of Binary Quadratic Forms Density Theorems L-Functions and Nonresidues Approximate Equations On Primitive Roots References Author Index Subject Index

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