The Theory of the Riemann Zeta-Function

by Titchmarsh, E. C.; Heath-brown, D. R.

• ISBN13: 9780198533696
• ISBN10: 0198533691
• Edition: 2nd
• Format: Paperback
• Copyright: 1987-02-05
• Publisher: Oxford University Press

Summary

The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects of the theory, starting from first principles and probing the function's own challenging theory, with the famous and still unsolved "Riemann hypothesis" at its heart. The second edition has been revised to include descriptions of work done in the last forty years and is updated with many additional references; it will provide stimulating reading for postgraduates and workers in analytic number theory and classical analysis.

Table of Contents

The Zeta Function and the Dirichlet Series Related to It

The Analytic Character of Zetas and the Functional Equation

The Theorem of Hadamard and De La Vallee Poussin, and Its Consequences

Approximate Formulae

The Order of Zetas in the Critical Strip VI. Vinogradov's Method

Mean-Value Theorems

(Capital Omega) Theorems

The General Distribution of Zeros

The Zeros on the Critical Line

The General Distribution of Values of Zetas

Divisor Problems

The Lindelof Hypothesis

Consequences of the Riemann Hypothesis

Calculations Relating to the Zeros

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