The Theory of the Riemann Zeta-Function [Paperback]

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.

I. The Zeta Function and the Dirichlet Series Related to It
II. The Analytic Character of Zetas and the Functional Equation
III. The Theorem of Hadamard and De La Vallee Poussin, and Its Consequences
IV. Approximate Formulae
V. The Order of Zetas in the Critical Strip
VI. Vinogradov's Method
VII. Mean-Value Theorems
VIII. (Capital Omega) Theorems
IX. The General Distribution of Zeros
X. The Zeros on the Critical Line
XI. The General Distribution of Values of Zetas
XII. Divisor Problems
XIII. The Lindel?f Hypothesis
XIV. Consequences of the Riemann Hypothesis
XV. Calculations Relating to the Zeros

The first edition of this classical treatise appeared in 1951 . . . Besides writing the updating and elucidating notes, covering all in all over 50 pages, the editor also has compiled a list of some 120 additional references to the more recent literature on the zeta-function. Thanks to the ample new material, this new edition makes very interesting reading, even for those who are familiar with the original. --Mathematical Reviews

Despite its age this is probably the most-cited book on the zeta function... The book is very comprehensive, and covers nearly anything anyone would want to know about the zeta function. -- MAA Reviews

A reprinting of this classic treatise with lҼ