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The theory of the Riemann zeta-function /

by Titchmarsh, E. C. (Edward Charles); Heath-Brown, D. R [edt].
Material type: materialTypeLabelBookSeries: Oxford science publications. Publisher: Oxford [Oxfordshire] : New York : Clarendon Press ; Oxford University Press, 1986Edition: 2nd ed.Description: x, 412 p. ; 24 cm.ISBN: 0198533691 (pbk.) :.Subject(s): Functions, ZetaOnline resources: Publisher description | Table of contents only
Contents:
The function [zeta](s) and the Dirichlet series related to it -- The analytic character of [zeta](s), and the functional equations -- The theorem of Hadamard and De La Vallée Poussin, and its consequences -- Approximate formulae -- The order of [zeta](s) in the critical strip -- Vinogradov's method -- Mean-value theorems -- [Omega]-theorems -- The general distribution of zeros -- The zeros on the critical line -- The general distribution of values of [zeta](s) -- Divisor problems -- The Lindelöf hypothesis -- Consequences of the Riemann hypothesis -- Calculations relating to the zeros.
Summary: The Riemann zeta-function is our most important tool in the study of prime numbers, and yet the famous "Riemann hypothesis" at its core remains unsolved. This book studies the theory from every angle and includes new material on recent work.
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515.56 T617 (Browse shelf) Available

Bibliography: p. [392]-412.

The function [zeta](s) and the Dirichlet series related to it --
The analytic character of [zeta](s), and the functional equations --
The theorem of Hadamard and De La Vallée Poussin, and its consequences --
Approximate formulae --
The order of [zeta](s) in the critical strip --
Vinogradov's method --
Mean-value theorems --
[Omega]-theorems --
The general distribution of zeros --
The zeros on the critical line --
The general distribution of values of [zeta](s) --
Divisor problems --
The Lindelöf hypothesis --
Consequences of the Riemann hypothesis --
Calculations relating to the zeros.

The Riemann zeta-function is our most important tool in the study of prime numbers, and yet the famous "Riemann hypothesis" at its core remains unsolved. This book studies the theory from every angle and includes new material on recent work.