The Theory of the Riemann Zeta-Function
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.
1100462715
The Theory of the Riemann Zeta-Function
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.
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The Theory of the Riemann Zeta-Function

The Theory of the Riemann Zeta-Function

The Theory of the Riemann Zeta-Function

The Theory of the Riemann Zeta-Function

Overview

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.

Product Details

ISBN-13: 9780198533696
Publisher: Oxford University Press
Publication date: 02/05/1987
Series: Oxford Science Publications Series
Edition description: REV
Pages: 424
Product dimensions: 9.24(w) x 6.18(h) x 1.04(d)

About the Author

Oxford University

Magdelen College, Oxford

Table of Contents

I. The Zeta Function and the Dirichlet Series Related to ItII. The Analytic Character of Zetas and the Functional EquationIII. The Theorem of Hadamard and De La Vallee Poussin, and Its ConsequencesIV. Approximate FormulaeV. The Order of Zetas in the Critical StripVI. Vinogradov's MethodVII. Mean-Value TheoremsVIII. (Capital Omega) TheoremsIX. The General Distribution of ZerosX. The Zeros on the Critical LineXI. The General Distribution of Values of ZetasXII. Divisor ProblemsXIII. The Lindelöf HypothesisXIV. Consequences of the Riemann HypothesisXV. Calculations Relating to the Zeros
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Related Subjects

Science & Technology
Mathematics
Number Theory
Science & Technology
Mathematics
Number Theory

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